Solved: Two wires are parallel, and one is directly above

Considering the nature of a water wave (see Figure 16.4), which of the following statements correctly describes how a fishing float moves on the surface of a lake when a wave passes beneath it? (a) It bobs up and down vertically. (b) It moves back and forth horizontally. (c) It moves in a vertical plane, exhibiting both motions described in (a) and (b) simultaneously

Suppose that the longitudinal wave in Figure 16.3c moves to the right at a speed of 1 m/s. Does one coil of the Slinky move a distance of 1 mm to the right in a time of 1 ms?

AM and FM radio waves are transverse waves consisting of electric and magnetic disturbances traveling at a speed of 3.00 108 m/s. A station broadcasts an AM radio wave whose frequency is 1230 103 Hz (1230 kHz on the dial) and an FM radio wave whose frequency is 91.9 106 Hz (91.9 MHz on the dial). Find the distance between adjacent crests in each wave. Rea

A sound wave (a periodic longitudinal wave) from a loudspeaker travels from air into water. The frequency of the wave does not change, because the loudspeaker producing the sound determines the frequency. The speed of sound in air is 343 m/s, whereas the speed in fresh water is 1482 m/s. When the sound wave enters the water, does its wavelength increase, decrease, or remain the same?

Transverse waves travel on each string of an electric guitar after the string is plucked (see Figure 16.8). The length of each string between its two fixed ends is 0.628 m, and the mass is 0.208 g for the highest pitched E string and 3.32 g for the lowest pitched E string. Each string is under a tension of 226 N. Find the speeds of the waves on the two strings.

As indicated in Figure 16.9, the speed of a transverse wave on a string is vwave, and the speed at which a string particle moves is vparticle. Which of the following statements is correct? (a) The speeds vwave and vparticle are identical. (b) The speeds vwave and vparticle are differen

One end of each of two identical strings is attached to a wall. Each string is being pulled equally tight by someone at the other end. A transverse pulse is sent traveling along string A. A bit later an identical pulse is sent traveling along string B. What, if anything, can be done to make the pulse on string B catch up with and pass the pulse on string A?

In Section 4.10 the concept of a massless rope is discussed. Considering Equation 16.2, would it take any time for a transverse wave to travel the length of a truly massless rope?

A wire is strung tightly between two immovable posts. Review Section 12.4 and decide whether the speed of a transverse wave on this wire would increase, decrease, or remain the same when the temperature increases. Ignore any change in the mass per unit length of the wire.

Examine Conceptual Example 3 before addressing this question. A wave moves on a string with a constant velocity. Does this mean that the particles of the string always have zero acceleration?

A rope of mass m is hanging down from the ceiling. Nothing is attached to the loose end of the rope. As a transverse wave travels upward on the rope, does the speed of the wave increase, decrease, or remain the same?

String I and string II have the same length. However, the mass of string I is twice the mass of string II, and the tension in string I is eight times the tension in string II. A wave of the same amplitude and frequency travels on each of these strings. Which of the drawings correctly shows the waves: (a) A (b) B (c) C?

In a traveling sound wave, are there any particles that are always at rest as the wave passes by?

Figure 16.18 shows an ultrasonic ruler that is used to measure the distance to a target, such as a wall. To initiate the measurement, the ruler generates a pulse of ultrasonic sound that travels to the wall and, much like an echo, reflects from it. The reflected pulse returns to the ruler, which measures the time it takes for the round-trip. Using a preset value for the speed of sound, the unit determines the distance to the wall and displays it on a digital readout. Suppose that the round-trip travel time is 20.0 ms on a day when the air temperature is 32 C. Assuming that air is an ideal diatomic gas and that the average molecular mass of air is 28.9 u, find the distance between the ultrasonic ruler and the wall.

In a thunderstorm, lightning and thunder occur nearly simultaneously. The light waves from the lightning travel at a speed of vlight 3.0  108 m/s, whereas the sound waves from the thunder travel at vsound 343 m/s. There is a rule of thumb for estimating how far away a storm is. After you see a lightning flash, count the seconds until you hear the thunder; divide the number of seconds by five to get the approximate distance (in miles) to the storm. In this rule, which of the two speeds plays a role? (a) Both vsound and vlight (b) Only vsound (c) Only vlight R

Do you expect an echo to return to you more quickly on a hot day or a cold day, other things being equal?

Carbon monoxide (CO), hydrogen (H2), and nitrogen (N2) may be treated as ideal gases. Each has the same temperature and nearly the same value for the ratio of the specific heat capacities at constant pressure and constant volume. In which two of the three gases is the speed of sound approximately the same?

Jell-O starts out as a liquid and then sets to a gel. As the Jell-O sets and becomes more solid, does the speed of sound in this material increase, decrease, or remain the same?

In Figure 16.21, 12 W of sound power passes perpendicularly through the surfaces labeled 1 and 2. These surfaces have areas of A1 4.0 m2 and A2 12 m2 . Determine the sound intensity at each surface and discuss why listener 2 hears a quieter sound than listener 1.

During a fireworks display, a rocket explodes high in the air above the observers. Assume that the sound spreads out uniformly in all directions and that reflections from the ground can be ignored. When the sound reaches listener 2 in Figure 16.23, who is r 2 640 m away from the explosion, the sound has an intensity of I2 0.10 W/m2 . What is the sound intensity detected by listener 1, who is r 1 160 m away from the explosion? R

Suppose that the person singing in the shower in Figure 16.24 produces a sound power P. Sound reflects from the surrounding shower stall. At a distance r in front of the person, does the expression I P/(4r 2) (Equation 16.9) (a) overestimate, (b) underestimate, or (c) give the correct total sound intensity?

Some animals rely on an acute sense of hearing for survival, and the visible parts of the ears on such animals are often relatively large. How does this anatomical feature help to increase the sensitivity of the animals hearing for low-intensity sounds?

A source is emitting sound uniformly in all directions. There are no reflections anywhere. A flat surface faces the source. Is the sound intensity the same at all points on the surface?

Audio system 1 produces an intensity level of 1 90.0 dB, and system 2 produces an intensity level of 2 93.0 dB. The corresponding intensities (in W/m2) are I1 and I2. Determine the ratio I2 /I1.

If two people talk simultaneously and each creates an intensity level of 65 dB at a certain point, does the total intensity level at this point equal 130 dB?

Two observation points are located at distances r1 and r2 from a source of sound. The sound spreads out uniformly from the source, and there are no reflecting surfaces in the environment. The sound intensity level at distance r2 is 6 dB less than the level at distance r1. (a) What is the ratio I2 /I1 of the sound intensities at the two distances? (b) What is the ratio r2 /r1 of the distances?

A high-speed train is traveling at a speed of 44.7 m/s (100 mi/h) when the engineer sounds the 415-Hz warning horn. The speed of sound is 343 m/s. What are the frequency and wavelength of the sound, as perceived by a person standing at a crossing, when the train is (a) approaching and (b) leaving the crossing?

A speedboat, starting from rest, moves along a straight line away from a dock. The boat has a constant acceleration of 3.00 m/s2 (see Figure 16.30). Attached to the dock is a siren that is producing a 755-Hz tone. If the air temperature is 20 C, what is the frequency of the sound heard by a person on the boat when the boats displacement from the dock is 45.0 m?

At a swimming pool, a music fan up on a diving platform is listening to a radio. As the radio is playing a tone that has a constant frequency fs, it is accidentally knocked off the platform. Describe the Doppler effect heard by (a) the person on the platform and (b) a person down below in the water. In each case, state whether the observed frequency fo is greater or smaller than fs and describe how fo changes (if it changes) as the radio falls.

When a car is at rest, its horn emits a frequency of 600 Hz. A person standing in the middle of the street with this car behind him hears the horn with a frequency of 580 Hz. Does he need to jump out of the way?

A source of sound produces the same frequency under water as it does in air. This source has the same velocity in air as it does under water. Consider the ratio fo /fs of the observed frequency fo to the source frequency fs. Is this ratio greater in air or under water when the source (a) approaches and (b) moves away from the observer?

Two cars, one behind the other, are traveling in the same direction at the same speed. Does either driver hear the others horn at a frequency that is different from the frequency heard when both cars are at rest?

When a truck is stationary, its horn produces a frequency of 500 Hz. You are driving your car, and this truck is following behind. You hear its horn at a frequency of 520 Hz. (a) Refer to Equation 16.15 and decide which algebraic sign should be used in the numerator and which in the denominator. (b) Which driver, if either, is driving faster?

What Determines the Speed of a Wave on a String?

Is the tension the same in each string?

Is the speed of each wave the same?

String 1 has a smaller mass and, hence, less inertia than string 2. Does this mean that the speed of the wave on string 1 is greater than the speed on string 2?

A siren, mounted on a tower, emits a sound whose frequency is 2140 Hz. A person is driving a car away from the tower at a speed of 27.0 m/s. As Figure 16.38 illustrates, the sound reaches the person by two paths: the sound reflected from a building in front of the car, and the sound coming directly from the siren. The speed of sound is 343 m/s. What frequency does the person hear for the (a) reflected and (b) direct sounds?

One way that the Doppler effect can arise is that the wavelength of the sound changes. For either the direct or the reflected sound, does the wavelength change?

Why does the driver hear a frequency for the reflected sound that is different from 2140 Hz, and is it greater than or smaller than 2140 Hz?

Why does the driver hear a frequency for the direct sound that is different from 2140 Hz, and is it greater than or smaller than 2140 Hz?

Domino toppling is an event in which a large number of dominoes are lined up close together and then allowed to topple, one after the other. The disturbance that propagates along the line of dominoes is ________________. (a) partly transverse and partly longitudinal (b) transverse (c) longitudinal

A transverse wave on a string has an amplitude A. A tiny spot on the string is colored red. As one cycle of the wave passes by, what is the total distance traveled by the red spot? (a) A (b) 2A (c) (d) 4A (e)

As a wave moves through a medium at a speed v, the particles of the medium move in simple harmonic motion about their undisturbed positions. The maximum speed of the simple harmonic motion is vmax. When the amplitude of the wave doubles, ________________. (a) v doubles, but vmax remains the same (b) v remains unchanged, but vmax doubles (c) both v and vmax remain unchanged (d) both v and vmax double

A rope is attached to a hook in the ceiling and is hanging straight down. The rope has a mass m, and nothing is attached to the free end of the rope. As a transverse wave travels down the rope from the top, ______________. (a) the speed of the wave does not change (b) the speed of the wave increases (c) the speed of the wave decreases

The equation that describes a transverse wave on a string is where y is the displacement of a string particle and x is the position of the particle on the string. The wave is traveling in the x direction. What is the speed v of the wave?

As the amplitude of a sound wave in air decreases to zero, ______________. (a) nothing happens to the condensations and rarefactions of the wave (b) the condensations and rarefactions of the wave occupy more and more distance along the direction in which the wave is traveling (c) the condensations of the wave disappear, but nothing happens to the rarefactions (d) nothing happens to the condensations of the wave, but the rarefactions disappear (e) both the condensations and the rarefactions of the wave disappear

An echo is sound that returns to you after being reflected from a distant surface (e.g., the side of a cliff). Assuming that the distances involved are the same, an echo under water and an echo in air return to you ______________. (a) at different times, the echo under water returning more slowly (b) at different times, the echo under water returning more quickly (c) at the same time

A horn on a boat sounds a warning, and the sound penetrates the water. How does the frequency of the sound in the air compare to its frequency in the water? How does the wavelength in the air compare to the wavelength in the water? (a) The frequency in the air is smaller than the frequency in the water, and the wavelength in the air is greater than the wavelength in the water. (b) The frequency in the air is greater than the frequency in the water, and the wavelength in the air is smaller than the wavelength in the water. (c) The frequency in the air is the same as the frequency in the water, and the wavelength in the air is the same as the wavelength in the water. (d) The frequency in the air is the same as the frequency in the water, and the wavelength in the air is smaller than the wavelength in the water. (e) The frequency in the air is the same as the frequency in the water, and the wavelength in the air is greater than the wavelength in the water.

A source emits sound uniformly in all directions. There are no reflections of the sound. At a distance of 12 m from the source, the intensity of the sound is 5.0 103 W/m2 . What is the total sound power P emitted by the source?

A source emits sound uniformly in all directions. There are no reflections of the sound. At a distance r1 from the source, the sound is 7.0 dB louder than it is at a distance r2 from the source. What is the ratio r1/r2?

A red car and a blue car can move along the same straight one-lane road. Both cars can move only at one speed when they move (e.g., 60 mph). The driver of the red car sounds his horn. In which one of the following situations does the driver of the blue car hear the highest horn frequency? (a) Both cars are moving at the same speed, and they are moving apart. (b) Both cars are moving in the same direction at the same speed. (c) Both cars are moving at the same speed, and they are moving toward each other. (d) The red car is moving toward the blue car, which is stationary. (e) The blue car is moving toward the red car, which is stationary.

What happens to the Doppler effect in air (i.e., the shift in frequency of a sound wave) as the temperature increases? (a) It is greater at higher temperatures, but only in the case of a moving source and a stationary observer. (b) It is greater at higher temperatures, but only in the case of a moving observer and a stationary source. (c) It is greater at higher temperatures than at lower temperatures. (d) It is less at higher temperatures than at lower temperatures. (e) The Doppler effect does not change as the temperature increases.

Light is an electromagnetic wave and travels at a speed of 3.00 108 m/s. The human eye is most sensitive to yellow-green light, which has a wavelength of 5.45 107 m. What is the frequency of this light?

Consider the freight train in Figure 16.6. Suppose that 15 boxcars pass by in a time of 12.0 s and each has a length of 14.0 m. (a) What is the frequency at which each boxcar passes? (b) What is the speed of the train?

A woman is standing in the ocean, and she notices that after a wave crest passes, five more crests pass in a time of 50.0 s. The distance between two successive crests is 32 m. Determine, if possible, the waves (a) period, (b) frequency, (c) wavelength, (d) speed, and (e) amplitude. If it is not possible to determine any of these quantities, then so state.

Tsunamis are fast-moving waves often generated by underwater earthquakes. In the deep ocean their amplitude is barely noticeable, but upon reaching shore, they can rise up to the astonishing height of a six-story building. One tsunami, generated off the Aleutian islands in Alaska, had a wavelength of 750 km and traveled a distance of 3700 km in 5.3 h. (a) What was the speed (in m/s) of the wave? For reference, the speed of a 747 jetliner is about 250 m/s. Find the waves (b) frequency and (c) period.

In Figure 16.2c the hand moves the end of the Slinky up and down through two complete cycles in one second. The wave moves along the Slinky at a speed of 0.50 m/s. Find the distance between two adjacent crests on the wave.

A person fishing from a pier observes that four wave crests pass by in 7.0 s and estimates the distance between two successive crests to be 4.0 m. The timing starts with the first crest and ends with the fourth. What is the speed of the wave?

Using the data in the graphs that accompany this problem, determine the speed of the wave.

A 3.49-rad/s (33 rpm) record has a 5.00-kHz tone cut in the groove. If the groove is located 0.100 m from the center of the record (see drawing), what is the wavelength in the groove?

The speed of a transverse wave on a string is 450 m/s, and the wavelength is 0.18 m. The amplitude of the wave is 2.0 mm. How much time is required for a particle of the string to move through a total distance of 1.0 km?

A jetskier is moving at 8.4 m/s in the direction in which the waves on a lake are moving. Each time he passes over a crest, he feels a bump. The bumping frequency is 1.2 Hz, and the crests are separated by 5.8 m. What is the wave speed?

A water-skier is moving at a speed of 12.0 m/s. When she skis in the same direction as a traveling wave, she springs upward every 0.600 s because of the wave crests. When she skis in the direction opposite to the direction in which the wave moves, she springs upward every 0.500 s in response to the crests. The speed of the skier is greater than the speed of the wave. Determine (a) the speed and (b) the wavelength of the wave.

The mass of a string is 5.0 103 kg, and it is stretched so that the tension in it is 180 N. A transverse wave traveling on this string has a frequency of 260 Hz and a wavelength of 0.60 m. What is the length of the string?

The middle C string on a piano is under a tension of 944 N. The period and wavelength of a wave on this string are 3.82 ms and 1.26 m, respectively. Find the linear density of the string.

A wire is stretched between two posts. Another wire is stretched between two posts that are twice as far apart. The tension in the wires is the same, and they have the same mass. A transverse wave travels on the shorter wire with a speed of 240 m/s. What would be the speed of the wave on the longer wire?

To measure the acceleration due to gravity on a distant planet, an astronaut hangs a 0.055-kg ball from the end of a wire. The wire has a length of 0.95 m and a linear density of 1.2 104 kg/m. Using electronic equipment, the astronaut measures the time for a transverse pulse to travel the length of the wire and obtains a value of 0.016 s. The mass of the wire is negligible compared to the mass of the ball. Determine the acceleration due to gravity.

Two wires are parallel, and one is directly above the other. Each has a length of 50.0 m and a mass per unit length of 0.020 kg/m. However, the tension in wire A is 6.00 102 N, and the tension in wire B is 3.00 102 N. Transverse wave pulses are generated simultaneously, one at the left end of wire A and one at the right end of wire B. The pulses travel toward each other. How much time does it take until the pulses pass each other? 1

The drawing shows two transverse waves traveling on strings. The linear density of each string is 0.065 kg/m. The tension is provided by a 26-N block that is hanging from the string. Find the speed of the wave in part (a) and in part (b) of the drawing.

A steel cable has a cross-sectional area 2.83 103 m2 and is kept under a tension of 1.00 104 N. The density of steel is 7860 kg/m3 . Note that this value is not the linear density of the cable. At what speed does a transverse wave move along the cable? *

The drawing shows a graph of two waves traveling to the right at the same speed. (a) Using the data in the drawing, determine the wavelength of each wave. (b) The speed of the waves is 12 m/s; calculate the frequency of each one. (c) What is the maximum speed for a particle attached to each wave?

Review Conceptual Example 3 before starting this problem. The amplitude of a transverse wave on a string is 4.5 cm. The ratio of the maximum particle speed to the speed of the wave is 3.1. What is the wavelength (in cm) of the wave?

The drawing shows a frictionless incline and pulley. The two blocks are connected by a wire (mass per unit length 0.0250 kg/m) and remain stationary. A transverse wave on the wire has a speed of 75.0 m/s. Neglecting the weight of the wire relative to the tension in the wire, find the masses m1 and m2 of the blocks.

A copper wire, whose cross-sectional area is 1.1 m2 , has a linear density of 9.8 kg/m and is strung between two walls. At the ambient temperature, a transverse wave travels with a speed of 46 m/s on this wire. The coefficient of linear expansion for copper is 17 and Youngs modulus for copper is 1.1 1011 N/m2 . What will be the speed of the wave when the temperature is lowered by 14 C ? Ignore any change in the linear density caused by the change in temperature. **

The drawing shows a 15.0-kg ball being whirled in a circular path on the end of a string. The motion occurs on a frictionless, horizontal table. The angular speed of the ball is 12.0 rad/s. The string has a mass of 0.0230 kg. How much time does it take for a wave on the string to travel from the center of the circle to the ball? Se

A wave traveling along the x axis is described mathematically by the equation y 0.17 sin (8.2t  0.54x), where y is the displacement (in meters), t is in seconds, and x is in meters. What is the speed of the wave?

A wave has the following properties: amplitude 0.37 m, period 0.77 s, wave speed 12 m/s. The wave is traveling in the x direction. What is the mathematical expression (similar to Equation 16.3 or 16.4) for the wave? 26

The drawing shows a graph that represents a transverse wave on a string. The wave is moving in the x direction with a speed of 0.15 m/s. Using the information contained in the graph, write the mathematical expression (similar to Equation 16.3 or 16.4) for the wave.

A wave traveling in the x direction has an amplitude of 0.35 m, a speed of 5.2 m/s, and a frequency of 14 Hz. Write the equation of the wave in the form given by either Equation 16.3 or 16.4.

A transverse wave is traveling on a string. The displacement y of a particle from its equilibrium position is given by y (0.021 m) sin (25t  2.0 x). Note that the phase angle 25t  2.0x is in radians, t is in seconds, and x is in meters. The linear density of the string is 1.6 kg /m. What is the tension in the string?

The tension in a string is 15 N, and its linear density is 0.85 kg/m. A wave on the string travels toward the x direction; it has an amplitude of 3.6 cm and a frequency of 12 Hz. What are the (a) speed and (b) wavelength of the wave? (c) Write down a mathematical expression (like Equation 16.3 or 16.4) for the wave, substituting numbers for the variables A, f, and .

A transverse wave on a string has an amplitude of 0.20 m and a frequency of 175 Hz. Consider the particle of the string at x 0 m. It begins with a displacement of y 0 m when t 0 s, according to Equation 16.3 or 16.4. How much time passes between the first two instants when this particle has a displacement of y 0.10 m? Sec

For research purposes a sonic buoy is tethered to the ocean floor and emits an infrasonic pulse of sound (speed 1522 m/s). The period of this sound is 71 ms. Determine the wavelength of the sound.

To navigate, a porpoise emits a sound wave that has a wavelength of 1.5 cm. The speed at which the wave travels in seawater is 1522 m/s. Find the period of the wave.

At what temperature is the speed of sound in helium (ideal gas,  1.67, atomic mass 4.003 u) the same as its speed in oxygen at 0 C? 3

Have you ever listened for an approaching train by kneeling next to a railroad track and putting your ear to the rail? Youngs modulus for steel is Y 2.0 1011 N/m2 , and the density of steel is  7860 kg/m3 . On a day when the temperature is 20 C, how many times greater is the speed of sound in the rail than in the air? 35

The speed of a sound in a container of hydrogen at 201 K is 1220 m/s. What would be the speed of sound if the temperature were raised to 405 K? Assume that hydrogen behaves like an ideal gas.

Suppose you are part of a team that is trying to break the sound barrier with a jet-powered car, which means that it must travel faster than the speed of sound in air. In the morning, the air temperature is 0 C, and the speed of sound is 331 m/s. What speed must your car exceed if it is to break the sound barrier when the temperature has risen to 43 C in the afternoon? Assume that air behaves like an ideal gas.

As the drawing illustrates, a siren can be made by blowing a jet of air through 20 equally spaced holes in a rotating disk. The time it takes for successive holes to move past the air jet is the period of the sound. The siren is to produce a 2200-Hz tone. What must be the angular speed (in rad/s) of the disk?

At a height of ten meters above the surface of a freshwater lake, a sound pulse is generated. The echo from the bottom of the lake returns to the point of origin 0.110 s later. The air and water temperature are 20 C. How deep is the lake?

An observer stands 25 m behind a marksman practicing at a rifle range. The marksman fires the rifle horizontally, the speed of the bullets is 840 m/s, and the air temperature is 20 C. How far does each bullet travel before the observer hears the report of the rifle? Assume that the bullets encounter no obstacles during this interval, and ignore both air resistance and the vertical component of the bullets motion.

An ultrasonic ruler, such as the one discussed in Example 4 in Section 16.6, displays the distance between the ruler and an object, such as a wall. The ruler sends out a pulse of ultrasonic sound and measures the time it takes for the pulse to reflect from the object and return. The ruler uses this time, along with a preset value for the speed of sound in air, to determine the distance. Suppose that you use this ruler under water, rather than in air. The actual distance from the ultrasonic ruler to an object is 25.0 m. The adiabatic bulk modulus and density of seawater are Bad 2.37 109 Pa and  1025 kg/m3 , respectively. Assume that the ruler uses a preset value of 343 m/s for the speed of sound in air. Determine the distance reading that the ruler displays. 4

An explosion occurs at the end of a pier. The sound reaches the other end of the pier by traveling through three media: air, fresh water, and a slender metal handrail. The speeds of sound in air, water, and the handrail are 343, 1482, and 5040 m/s, respectively. The sound travels a distance of 125 m in each medium. (a) Through which medium does the sound arrive first, second, and third? (b) After the first sound arrives, how much later do the second and third sounds arrive?

A hunter is standing on flat ground between two vertical cliffs that are directly opposite one another. He is closer to one cliff than to the other. He fires a gun and, after a while, hears three echoes. The second echo arrives 1.6 s after the first, and the third echo arrives 1.1 s after the second. Assuming that the speed of sound is 343 m/s and that there are no reflections of sound from the ground, find the distance between the cliffs.

A monatomic ideal gas ( 1.67) is contained within a box whose volume is 2.5 m3 . The pressure of the gas is 3.5 105 Pa. The total mass of the gas is 2.3 kg. Find the speed of sound in the gas. *

A long slender bar is made from an unknown material. The length of the bar is 0.83 m, its cross-sectional area is 1.3 m2 , and its mass is 2.1 kg. A sound wave travels from one end of the bar to the other end in 1.9 s. From which one of the materials listed in Table 10.1 is the bar most likely to be made? *

As the drawing shows, one microphone is located at the origin, and a second microphone is located on the y axis. The microphones are separated by a distance of D 1.50 m. A source of sound is located on the x axis, its distances from microphones 1 and 2 being L1 and L2, respectively. The speed of sound is 343 m/s. The sound reaches microphone 1 first, and then, 1.46 ms later, it reaches microphone 2. Find the distances L1 and L2 .

When an earthquake occurs, two types of sound waves are generated and travel through the earth. The primary, or P, wave has a speed of about 8.0 km/s and the secondary, or S, wave has a speed of about 4.5 km/s. A seismograph, located some distance away, records the arrival of the P wave and then, 78 s later, records the arrival of the S wave. Assuming that the waves travel in a straight line, how far is the seismograph from the earthquake?

Consult Multiple-Concept Example 4 in order to review a model for solving this type of problem. Suppose that you are standing by the side of a road in the Sahara desert where the temperature has reached a hot 56 C (130 F). A truck, traveling at a constant speed, passes by. After 4.00 s have elapsed, you use the ultrasonic ruler discussed in Example 4 to measure the distance to the truck. A sound pulse leaves the ultrasonic ruler and returns 0.120 s later. Assume that the average molecular mass of air is 28.9 u, air is an ideal diatomic gas , and the truck moves a negligible distance in the time it takes for the sound pulse to reach it. Determine how fast the truck is moving.

In a mixture of argon (atomic mass 39.9 u) and neon (atomic mass 20.2 u), the speed of sound is 363 m/s at 3.00  102 K. Assume that both monatomic gases behave as ideal gases. Find the percentage of the atoms that are argon and the percentage that are neon. *

Refer to Multiple-Concept Example 4 for a review of the concepts that play roles in this problem. Civil engineers use a transit theodolite when surveying. One version of this device determines distance by measuring the time required for an ultrasonic pulse to reach a target, reflect from it, and return. When calibrated properly, the device uses the speed of sound appropriate for the ambient air temperature to determine the distance between the theodolite and the target. Suppose a theodolite is calibrated so that it gives the correct value for a distance when used at a temperature of 291 K. When used at a temperature of 298 K, however, the device gives an incorrect value for the same distance. What percentage error would there be in the incorrect value measured by the theodolite? Is the incorrect value smaller than or greater than the correct value? Assume that air behaves as an ideal gas, so that Equation 16.5 applies.

As a prank, someone drops a water-filled balloon out of a window. The balloon is released from rest at a height of 10.0 m above the ears of a man who is the target. Then, because of a guilty conscience, the prankster shouts a warning after the balloon is released. The warning will do no good, however, if shouted after the balloon reaches a certain point, even if the man could react infinitely quickly. Assuming that the air temperature is 20 C and ignoring the effect of air resistance on the balloon, determine how far above the mans ears this point is.

A typical adult ear has a surface area of 2.1  m2 . The sound intensity during a normal conversation is about 3.2  W/m2 at the listeners ear. Assume that the sound strikes the surface of the ear perpendicularly. How much power is intercepted by the ear?

At a distance of 3.8 m from a siren, the sound intensity is 3.6  W/m2 . Assuming that the siren radiates sound uniformly in all directions, find the total power radiated.

A source of sound is located at the center of two concentric spheres, parts of which are shown in the drawing. The source emits sound uniformly in all directions. On the spheres are drawn three small patches that may or may not have equal areas. However, the same sound power passes through each patch. The source produces 2.3 W of sound power, and the radii of the concentric spheres are rA 0.60 m and 1

Suppose that in Conceptual Example 8 (see Figure 16.24) the person is producing 1.1 mW of sound power. Some of the sound is reflected from the floor and ceiling. The intensity of this reflected sound at a distance of 3.0 m from the source is 4.4  W/m2 . What is the total sound intensity due to both the direct and reflected sounds, at this point?

Suppose that a public address system emits sound uniformly in all directions and that there are no reflections. The intensity at a location 22 m away from the sound source is 3.0  104 W/m2 . What is the intensity at a spot that is 78 m away?

A loudspeaker has a circular opening with a radius of 0.0950 m. The electrical power needed to operate the speaker is 25.0 W. The average sound intensity at the opening is 17.5 W/m2 . What percentage of the electrical power is converted by the speaker into sound power?

A man stands at the midpoint between two speakers that are broadcasting an amplified static hiss uniformly in all directions. The speakers are 30.0 m apart and the total power of the sound coming from each speaker is 0.500 W. Find the total sound intensity that the man hears (a) when he is at his initial position halfway between the speakers, and (b) after he has walked 4.0 m directly toward one of the speakers.

A dish of lasagna is being heated in a microwave oven. The effective area of the lasagna that is exposed to the microwaves is 2.2  102 m2 . The mass of the lasagna is 0.35 kg, and its specific heat capacity is 3200 J/(kg C). The temperature rises by 72 C in 8.0 minutes. What is the intensity of the microwaves in the oven? *

Two sources of sound are located on the x axis, and each emits power uniformly in all directions. There are no reflections. One source is positioned at the origin and the other at x 123 m. The source at the origin emits four times as much power as the other source. Where on the x axis are the two sounds equal in intensity? Note that there are two answers.

Deep ultrasonic heating is used to promote healing of torn tendons. It is produced by applying ultrasonic sound over the affected area of the body. The sound transducer (generator) is circular with a radius of 1.8 cm, and it produces a sound intensity of 5.9  103 W/m2 . How much time is required for the transducer to emit 4800 J of sound energy?

A rocket, starting from rest, travels straight up with an acceleration of 58.0 m/s2 . When the rocket is at a height of 562 m, it produces sound that eventually reaches a ground-based monitoring station directly below. The sound is emitted uniformly in all directions. The monitoring station measures a sound intensity I. Later, the station measures an intensity There are no reflections. Assuming that the speed of sound is 343 m/s, find the time that has elapsed between the two measurements

A woman stands a distance d from a loud motor that emits sound uniformly in all directions. The sound intensity at her position is an uncomfortable 3.2 103 W/m2 . There are no reflections. At a position twice as far from the motor, what are (a) the sound intensity and (b) the sound intensity level relative to the threshold of hearing?

The volume control on a surround-sound amplifier is adjusted so the sound intensity level at the listening position increases from 23 to 61 dB. What is the ratio of the final sound intensity to the original sound intensity?

A middle-aged man typically has poorer hearing than a middle-aged woman. In one case a woman can just begin to hear a musical tone, while a man can just begin to hear the tone only when its intensity level is increased by 7.8 dB relative to the just-audible intensity level for the woman. What is the ratio of the sound intensity just detected by the man to the sound intensity just detected by the woman?

Using an intensity of 1 1012 W/m2 as a reference, the threshold of hearing for an average young person is 0 dB. Person 1 and person 2, who are not average, have thresholds of hearing that are 1 8.00 dB and 2 12.0 dB. What is the ratio I1 /I2 of the sound intensity I1 when person 1 hears the sound at his own threshold of hearing compared to the sound intensity I2 when person 2 hears the sound at his own threshold of hearing? 67

A listener doubles his distance from a source that emits sound uniformly in all directions. There are no reflections. By how many decibels does the sound intensity level change?

Sound is passing perpendicularly through an open window whose dimensions are 1.1 m 0.75 m. The sound intensity level is 95 dB above the threshold of hearing. How much sound energy comes through the window in one hour?

The bellow of a territorial bull hippopotamus has been measured at 115 dB above the threshold of hearing. What is the sound intensity?

Hearing damage may occur when a person is exposed to a sound intensity level of 90.0 dB (relative to the threshold of hearing) for a period of 9.0 hours. One particular eardrum has an area of 2.0 104 m2 . How much sound energy is incident on this eardrum during this time?

When one person shouts at a football game, the sound intensity level at the center of the field is 60.0 dB. When all the people shout together, the intensity level increases to 109 dB. Assuming that each person generates the same sound intensity at the center of the field, how many people are at the game?

Review Conceptual Example 8 as background for this problem. A loudspeaker is generating sound in a room. At a certain point, the sound waves coming directly from the speaker (without reflecting from the walls) create an intensity level of 75.0 dB. The waves reflected from the walls create, by themselves, an intensity level of 72.0 dB at the same point. What is the total intensity level? (Hint: The answer is not 147.0 dB.)

A portable radio is sitting at the edge of a balcony 5.1 m above the ground. The unit is emitting sound uniformly in all directions. By accident, it falls from rest off the balcony and continues to play on the way down. A gardener is working in a flower bed directly below the falling unit. From the instant the unit begins to fall, how much time is required for the sound intensity level heard by the gardener to increase by 10.0 dB?

A source emits sound uniformly in all directions. A radial line is drawn from this source. On this line, determine the positions of two points, 1.00 m apart, such that the intensity level at one point is 2.00 dB greater than the intensity level at the other.

Suppose that when a certain sound intensity level (in dB) triples, the sound intensity (in W/m2) also triples. Determine this sound intensity level.

A bird is flying directly toward a stationary bird-watcher and emits a frequency of 1250 Hz. The bird-watcher, however, hears a frequency of 1290 Hz. What is the speed of the bird, expressed as a percentage of the speed of sound?

From a vantage point very close to the track at a stock car race, you hear the sound emitted by a moving car. You detect a frequency that is 0.86 times as small as the frequency emitted by the car when it is stationary. The speed of sound is 343 m/s. What is the speed of the car?

Dolphins emit clicks of sound for communication and echolocation. A marine biologist is monitoring a dolphin swimming in seawater where the speed of sound is 1522 m/s. When the dolphin is swimming directly away at 8.0 m/s, the marine biologist measures the number of clicks occurring per second to be at a frequency of 2500 Hz. What is the difference (in Hz) between this frequency and the number of clicks per second actually emitted by the dolphin?

A convertible moves toward you and then passes you; all the while, its loudspeakers are producing a sound. The speed of the car is a constant 9.00 m/s, and the speed of sound is 343 m/s. What is the ratio of the frequency you hear while the car is approaching to the frequency you hear while the car is moving away?

The security alarm on a parked car goes off and produces a frequency of 960 Hz. The speed of sound is 343 m/s. As you drive toward this parked car, pass it, and drive away, you observe the frequency to change by 95 Hz. At what speed are you driving?

A car is parked 20.0 m directly south of a railroad crossing. A train is approaching the crossing from the west, headed directly east at a speed of 55.0 m/s. The train sounds a short blast of its 289-Hz horn when it reaches a point 20.0 m west of the crossing. What frequency does the cars driver hear when the horn blast reaches the car? The speed of sound in air is 343 m/s. (Hint: Assume that only the component of the trains velocity that is directed toward the car affects the frequency heard by the driver.)

A loudspeaker in a parked car is producing sound whose frequency is 20 510 Hz. A healthy young person with normal hearing is standing nearby on the sidewalk but cannot hear the sound because the frequency is too high. When the car is moving, however, this person can hear the sound. (a) Is the car moving toward or away from the person? Why? (b) If the speed of sound is 343 m/s, what is the minimum speed of the moving car?

Two trucks travel at the same speed. They are far apart on adjacent lanes and approach each other essentially head-on. One driver hears the horn of the other truck at a frequency that is 1.14 times the frequency he hears when the trucks are stationary. The speed of sound is 343 m/s. At what speed is each truck moving?

Multiple-Concept Example 11 provides a model for solving this type of problem. A wireless transmitting microphone is mounted on a small platform that can roll down an incline, directly away from a loudspeaker that is mounted at the top of the incline. The loudspeaker broadcasts a tone that has a fixed frequency of 1.000 104 Hz, and the speed of sound is 343 m/s. At a time of 1.5 s following the release of the platform, the microphone detects a frequency of 9939 Hz. At a time of 3.5 s following the release of the platform, the microphone detects a frequency of 9857 Hz. What is the acceleration (assumed constant) of the platform?

Consult Multiple-Concept Example 11 in order to review a model for solving this type of problem. A car is accelerating while its horn is sounding. Just after the car passes a stationary person, the person hears a frequency of 966.0 Hz. Fourteen seconds later, the frequency heard by the person has decreased to 912.0 Hz. When the car is stationary, its horn emits a sound whose frequency is 1.00 103 Hz. The speed of sound is 343 m/s. What is the acceleration of the car?

The siren on an ambulance is emitting a sound whose frequency is 2450 Hz. The speed of sound is 343 m/s. (a) If the ambulance is stationary and you (the observer) are sitting in a parked car, what are the wavelength and the frequency of the sound you hear? (b) Suppose that the ambulance is moving toward you at a speed of 26.8 m/s. Determine the wavelength and the frequency of the sound you hear. (c) If the ambulance is moving toward you at a speed of 26.8 m/s and you are moving toward it at a speed of 14.0 m/s, find the wavelength and frequency of the sound you hear.

Two submarines are under water and approaching each other head-on. Sub A has a speed of 12 m/s and sub B has a speed of 8 m/s. Sub A sends out a 1550-Hz sonar wave that travels at a speed of 1522 m/s. (a) What is the frequency detected by sub B? (b) Part of the sonar wave is reflected from sub B and returns to sub A. What frequency does sub A detect for this reflected wave?

A microphone is attached to a spring that is suspended from the ceiling, as the drawing indicates. Directly below on the floor is a stationary 440-Hz source of sound. The microphone vibrates up and down in simple harmonic motion with a period of 2.0 s. The difference between the maximum and minimum sound frequencies detected by the microphone is 2.1 Hz. Ignoring any reflections of sound in the room and using 343 m/s for the speed of sound, determine the amplitude of the simple harmonic motion.

A recording engineer works in a soundproofed room that is 44.0 dB quieter than the outside. If the sound intensity that leaks into the room is 1.20 1010 W/m2 , what is the intensity outside?

A sound wave travels in air toward the surface of a freshwater lake and enters into the water. The frequency of the sound does not change when the sound enters the water. The wavelength of the sound is 2.74 m in the air, and the temperature of both the air and the water is 20 C. What is the wavelength in the water?

At 20 C the densities of fresh water and ethyl alcohol are, respectively, 998 and 789 kg/m3 . Find the ratio of the adiabatic bulk modulus of fresh water to the adiabatic bulk modulus of ethyl alcohol at 20 C.

You are flying in an ultralight aircraft at a speed of 39 m/s. An eagle, whose speed is 18 m/s, is flying directly toward you. Each of the given speeds is relative to the ground. The eagle emits a shrill cry whose frequency is 3400 Hz. The speed of sound is 330 m/s. What frequency do you hear?

Suppose that the linear density of the A string on a violin is 7.8 kg/m. A wave on the string has a frequency of 440 Hz and a wavelength of 65 cm. What is the tension in the string? 9

A car driving along a highway at a speed of 23 m/s strays onto the shoulder. Evenly spaced parallel grooves called rumble strips are carved into the pavement of the shoulder. Rolling over the rumble strips causes the cars wheels to oscillate up and down at a frequency of 82 Hz. How far apart are the centers of adjacent rumble-strip grooves?

When Gloria wears her hearing aid, the sound intensity level increases by 30.0 dB. By what factor does the sound intensity increase?

The average sound intensity inside a busy neighborhood restaurant is 3.2 W/m2 . How much energy goes into each ear (area 2.1 103 m2 ) during a one-hour meal? 97

Suppose that the amplitude and frequency of the transverse wave in Figure 16.2c are, respectively, 1.3 cm and 5.0 Hz. Find the total vertical distance (in cm) through which the colored dot moves in 3.0 s.

A bat emits a sound whose frequency is 91 kHz. The speed of sound in air at 20.0 C is 343 m/s. However, the air temperature is 35 C, so the speed of sound is not 343 m/s. Assume that air behaves like an ideal gas, and find the wavelength of the sound.

You are riding your bicycle directly away from a stationary source of sound and hear a frequency that is 1.0% lower than the emitted frequency. The speed of sound is 343 m/s. What is your speed?

Argon (molecular mass 39.9 u) is a monatomic gas. Assuming that it behaves like an ideal gas at 298 K ( 1.67), find (a) the rms speed of argon atoms and (b) the speed of sound in argon. 10

The sound intensity level at a rock concert is 115 dB, while that at a jazz fest is 95 dB. Determine the ratio of the sound intensity at the rock concert to the sound intensity at the jazz fest.

An amplified guitar has a sound intensity level that is 14 dB greater than the same unamplified sound. What is the ratio of the amplified intensity to the unamplified intensity?

In a discussion person A is talking 1.5 dB louder than person B, and person C is talking 2.7 dB louder than person A. What is the ratio of the sound intensity of person C to the sound intensity of person B?

In Figure 16.3c the colored dot exhibits simple harmonic motion as the longitudinal wave passes. The wave has an amplitude of 5.4 m and a frequency of 4.0 Hz. Find the maximum acceleration of the dot.

(a) A uniform rope of mass m and length L is hanging straight down from the ceiling. A small-amplitude transverse wave is sent up the rope from the bottom end. Derive an expression that gives the speed v of the wave on the rope in terms of the distance y above the bottom end of the rope and the magnitude g of the acceleration due to gravity. (b) Use the expression that you have derived to calculate the speeds at distances of 0.50 m and 2.0 m above the bottom end of the rope.

A spider hangs from a strand of silk whose radius is 4.0 106 m. The density of the silk is 1300 kg/m3 . When the spider moves, waves travel along the strand of silk at a speed of 280 m/s. Ignore the mass of the silk strand, and determine the mass of the spider.

Two blocks are connected by a wire that has a mass per unit length of 8.50 kg/m. One block has a mass of 19.0 kg, and the other has a mass of 42.0 kg. These blocks are being pulled across a horizontal frictionless floor by a horizontal force that is applied to the less massive block. A transverse wave travels on the wire between the blocks with a speed of 352 m/s (relative to the wire). The mass of the wire is negligible compared to the mass of the blocks. Find the magnitude of .

A member of an aircraft maintenance crew wears protective earplugs that reduce the sound intensity by a factor of 350. When a jet aircraft is taking off, the sound intensity level experienced by the crew member is 88 dB. What sound intensity level would the crew member experience if he removed the protective earplugs?

A jet is flying horizontally, as the drawing shows. When the plane is directly overhead at B, a person on the ground hears the sound coming from A in the drawing. The average temperature of the air is 20 C. If the speed of the plane at A is 164 m/s, what is its speed at B, assuming that it has a constant acceleration?

Review Multiple-Concept Example 4 for background pertinent to this problem. A team of geophysicists is standing on the ground. Beneath their feet, at an unknown distance, is the ceiling of a cavern. The floor of the cavern is a distance h below this ceiling. To measure h, the team places microphones on the ground. At t 0 s, a sound pulse is sent straight downward through the ground and into the cavern. When this pulse reaches the ceiling of the cavern, one part of it is reflected back toward the microphones, and a second part continues downward, eventually to be reflected from the cavern floor. The sound reflected from the cavern ceiling reaches the microphones at t 0.0245 s, and the sound reflected from the cavern floor arrives at t 0.0437 s. The cavern is presumed to be filled with air at a temperature of 9 C. Assuming that air behaves like an ideal gas, what is the height h of the cavern? A

A sound wave travels twice as far in neon (Ne) as it does in krypton (Kr) in the same time interval. Both neon and krypton can be treated as monatomic ideal gases. The atomic mass of neon is 20.2 u, and the atomic mass of krypton is 83.8 u. The temperature of the krypton is 293 K. What is the temperature of the neon?