A wave traveling along the x axis is described

Light is an electromagnetic wave and travels at a speed of 3.00 3 108 m/s. The human eye is most sensitive to yellow-green light, which has a wavelength of 5.45 3 1027 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 fi shing 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 fi rst 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 (331 3 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 3 1023 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 3 1024 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 3 102 N, and the tension in wire B is 3.00 3 102 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?

The drawing shows two transverse waves traveling on strings. The linear density of each string is \(0.065 \mathrm{~kg} / \mathrm{m}\). 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 3 1023 m2 and is kept under a tension of 1.00 3 104 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 5 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, fi nd the masses m1 and m2 of the blocks.

A copper wire, whose cross-sectional area is 1.1 3 1026 m2 , has a linear density of 9.8 3 1023 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 coeffi cient of linear expansion for copper is 17 3 1026 (C)21 , and Youngs modulus for copper is 1.1 3 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 v 5 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?

A wave traveling along the x axis is described mathematically by the equation y 5 0.17 sin (8.2pt 1 0.54px), 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 5 0.37 m, period 5 0.77 s, wave speed 5 12 m/s. The wave is traveling in the 2x direction. What is the mathematical expression (similar to Equation 16.3 or 16.4) for the wave?

The drawing shows a graph that represents a transverse wave on a string. The wave is moving in the 1x 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 1x 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 5 (0.021 m) sin (25t 2 2.0 x). Note that the phase angle 25t 2 2.0x is in radians, t is in seconds, and x is in meters. The linear density of the string is 1.6 3 1022 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 2x 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 l.

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 5 0 m. It begins with a displacement of y 5 0 m when t 5 0 s, according to Equation 16.3 or 16.4. How much time passes between the fi rst two instants when this particle has a displacement of y 5 0.10 m?

For research purposes a sonic buoy is tethered to the ocean fl oor and emits an infrasonic pulse of sound (speed 5 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, g 5 1.67, atomic mass 5 4.003 u) the same as its speed in oxygen at 0 8C?

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 5 2.0 3 1011 N/m2 , and the density of steel is r 5 7860 kg/m3 . On a day when the temperature is 20 8C, how many times greater is the speed of sound in the rail than in the air?

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 8C 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 v (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 8C. How deep is the lake?

An observer stands 25 m behind a marksman practicing at a rifl e range. The marksman fi res the rifl e horizontally, the speed of the bullets is 840 m/s, and the air temperature is 20 8C. How far does each bullet travel before the observer hears the report of the rifl e? 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 refl ect 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 5 2.37 3 109 Pa and r 5 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.

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 fi rst, second, and third? (b) After the fi rst sound arrives, how much later do the second and third sounds arrive?

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?

A hunter is standing on fl at ground between two vertical cliff s that are directly opposite one another. He is closer to one cliff than to the other. He fi res a gun and, after a while, hears three echoes. The second echo arrives 1.6 s after the fi rst, 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 refl ections of sound from the ground, fi nd the distance between the cliff s.

A monatomic ideal gas (g 5 1.67) is contained within a box whose volume is 2.5 m3 . The pressure of the gas is 3.5 3 105 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 3 1024 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 3 1024 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 1y axis. The microphones are separated by a distance of D 5 1.50 m. A source of sound is located on the 1x 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 fi rst, 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 8C (130 8F). 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 (g 5 7 5 ), 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 5 39.9 u) and neon (atomic mass 5 20.2 u), the speed of sound is 363 m/s at 3.00 3 102 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, refl ect 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-fi lled 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 infi nitely quickly. Assuming that the air temperature is 20 8C and ignoring the eff ect 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 3 1023 m2 . The sound intensity during a normal conversation is about 3.2 3 1026 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 3 1022 W/m2 . Assuming that the siren radiates sound uniformly in all directions, fi nd 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 5 0.60 m and rB 5 0.80 m. (a) Determine the sound intensity at each of the three patches. (b) The sound power that passes through each of the patches is 1.8 3 1023 W. Find the area of each patch.

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 refl ected from the fl oor and ceiling. The intensity of this refl ected sound at a distance of 3.0 m from the source is 4.4 3 1026 W/m2 . What is the total sound intensity due to both the direct and refl ected sounds, at this point?

Suppose that a public address system emits sound uniformly in all directions and that there are no refl ections. The intensity at a location 22 m away from the sound source is 3.0 3 1024 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 amplifi ed 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 3 1022 m2 . The mass of the lasagna is 0.35 kg, and its specifi c heat capacity is 3200 J/(kg ? C8). The temperature rises by 72 C8 in 8.0 minutes. What is the intensity of the microwaves in the oven?

wo sources of sound are located on the x axis, and each emits power uniformly in all directions. There are no refl ections. One source is positioned at the origin and the other at x 5 1123 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 aff ected 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 3 103 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 1 3 I. There are no refl ections. Assuming that the speed of sound is 343 m/s, fi nd 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 3 1023 W/m2 . There are no refl ections. 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 amplifi er is adjusted so the sound intensity level at the listening position increases from 23 to 61 dB. What is the ratio of the fi nal 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 3 10212 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 b1 5 28.00 dB and b2 5 112.0 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?

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

Sound is passing perpendicularly through an open window whose dimensions are 1.1 m 3 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 3 1024 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 fi eld 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 fi eld, 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 refl ecting from the walls) create an intensity level of 75.0 dB. The waves refl ected 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 fl ower 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 fl ying 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 diff erence (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 aff ects 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?

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 fi xed frequency of 1.000 3 104 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?

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 3 103 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, fi nd 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 refl ected from sub B and returns to sub A. What frequency does sub A detect for this refl ected wave?

A microphone is attached to a spring that is suspended from the ceiling, as the drawing indicates. Directly below on the fl oor 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 diff erence between the maximum and minimum sound frequencies detected by the microphone is 2.1 Hz. Ignoring any refl ections 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 3 10210 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 8C. What is the wavelength in the water?

At 20 8C 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 8C.

You are fl ying in an ultralight aircraft at a speed of 39 m/s. An eagle, whose speed is 18 m/s, is fl ying 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 3 1024 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?

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 3 1025 W/m2 . How much energy goes into each ear (area 5 2.1 3 1023 m2 ) during a one-hour meal?

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 8C is 343 m/s. However, the air temperature is 35 8C, so the speed of sound is not 343 m/s. Assume that air behaves like an ideal gas, and fi nd 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 5 39.9 u) is a monatomic gas. Assuming that it behaves like an ideal gas at 298 K (g 5 1.67), fi nd (a) the rms speed of argon atoms and (b) the speed of sound in argon.

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 amplifi ed guitar has a sound intensity level that is 14 dB greater than the same unamplifi ed sound. What is the ratio of the amplifi ed intensity to the unamplifi ed 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 3 1023 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 3 1026 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 3 1024 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 fl oor by a horizontal force P B 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 P B .

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 fl ying 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 8C. 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 fl oor of the cavern is a distance h below this ceiling. To measure h, the team places microphones on the ground. At t 5 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 refl ected from the cavern fl oor. The sound refl ected from the cavern ceiling reaches the microphones at t 5 0.0245 s, and the sound refl ected from the cavern fl oor arrives at t 5 0.0437 s. The cavern is presumed to be fi lled with air at a temperature of 9 8C. Assuming that air behaves like an ideal gas, what is the height h of the cavern?

A speedboat, starting from rest, moves along a straight line away from a dock. The boat has a constant acceleration of 13.00 m/s2 (see the fi gure). Attached to the dock is a siren that is producing a 755-Hz tone. If the air temperature is 20 8C, what is the frequency of the sound heard by a person on the boat when the boats displacement from the dock is 145.0 m?

The fi gure shows waves traveling on two strings. Each string is attached to a wall at one end and to a box that has a weight of 28.0 N at the other end. String 1 has a mass of 8.00 g and a length of 4.00 cm, and string 2 has a mass of 12.0 g and a length of 8.00 cm. Concepts: (i) Is the tension the same in each string? (ii) Is the speed of each wave the same? (iii) 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? Calculations: Determine the speed of the wave on each string.

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 the fi gure illustrates, the sound reaches the person by two paths: the sound refl ected from the building in front of the car, and the sound coming directly from the siren. The speed of sound is 343 m/s. Concepts: (i) One way that the Doppler eff ect can arise is that the wavelength of the sound changes. For either the direct or refl ected sound, does the wavelength change? (ii) Why does the driver hear a frequency for the refl ected sound that is diff erent from 2140 Hz, and is it greater or smaller than 2140 Hz? (iii) Why does the driver hear a frequency for the direct sound that is diff erent from 2140 Hz, and is it greater or smaller than 2140 Hz? Calculations: What frequency does the person hear for the (a) refl ected and (b) direct sound?