Solved: If the speed of a wave doubles while the frequency

Problem 1E Does the period of a pendulum depend on the mass of the bob? On the length of the string?

What is the frequency, in hertz, that corresponds to each of the following periods? (a) 0.10 s (b) 5 s (c) 1/60 s

Problem 1R All the waves shown have the same speed in the same medium. Use a ruler and rank these waves from most to least for a. amplitude. ________________ b. wavelength. ________________ c. frequency. ________________ d. period.

Problem 1RQ What is a wiggle in time called? What do you call a wiggle in space and time?

Problem 2E A heavy person and a light person swing to and fro on swings of the same length. Who has the longer period?

Problem 2P What is the period, in seconds, that corresponds to each of the following frequencies? (a) 10 Hz ________________ (b) 0.2 Hz ________________ (c) 60 Hz

Shown above right are four different pairs of transverse wave pulses that move toward each other. At some point in time, the pulses meet and interact (interfere) with each other. Rank the four cases, from most to least, on the basis of the height of the peak that results when the centers of the pulses coincide.

Problem 2RQ What is the source of all waves?

Problem 3E If a pendulum is shortened, does its frequency increase or decrease? What about its period?

Problem 3P A skipper on a boar notices wave crests passing his anchor chain every 5 s. He estimates the distance between wave crests to be 15 m. He also correctly estimates the speed of the waves. Show that this speed is 3 m/s.

Problem 3R The siren of a fire engine is heard in situations A, B, and C. Rank the pitch heard, from greatest to least, when the fire engine is traveling a. toward the listener at 30 km/h. ________________ b. toward the listener at 50 km/h. ________________ c. away from the listener at 20 km/h

Problem 3RQ What is meant by the period of a pendulum?

Problem 4E A grandfather pendulum clock keeps perfect time. Then it is relocated to a summer home high in the mountains. Does it run faster, slower, or the same? Explain.

A weight suspended from a spring is seen to bob up and down over a distance of \(20 \mathrm{~cm}\) twice each second. What is its frequency? Its period? Its amplitude?

Problem 4R The shock waves A, B, C are produced by supersonic aircraft. Rank their speeds from greatest to least.

Problem 4RQ Which has the longer period, a short or a long pendulum?

Problem 5E You pick up an empty briefcase and let it swing to and fro at its natural frequency. If the case were filled with books, would the natural frequency be lower, greater, or the same as before?

Problem 5P A mosquito flaps its wings 600 vibrations per second, which produces the annoying 600-Hz buzz. Given that the speed of sound is 340 m/s, how far does the sound travel between wing beats? In other words, find the wavelength of the mosquito’s sound.

Problem 5RQ How is a sine curve related to a wave?

Problem 6E Is the time required to swing to and fro (the period) on a playground swing longer or shorter when you stand rather than sit? Explain.

Problem 6P On a keyboard, you strike middle C, whose frequency is 256 Hz. (a) What is the period of one vibration of this tone? ________________ (b) As the sound leaves the instrument at a speed of 340 m/s, what is its wavelength in air?

Problem 6RQ Distinguish between these different aspects of a wave: period, amplitude, wavelength, and frequency.

Problem 7E What happens to the period of a wave when the frequency decreases?

Problem 7P As shown in the drawing, the half-angle of the shock wave cone generated by a supersonic airplane is 45°. What is the speed of the plane relative to the speed of sound?

Problem 7RQ How many vibrations per second are represented in a radio wave of 101.7 MHz?

Problem 8E Does it make sense that the mass of a bob in a simple pendulum doesn’t affect the frequency of the pendulum? Defend your answer.

Problem 8P An astronaut on the Moon attaches a small brass ball to a 1.00-m length of string and makes a simple pendulum. She times 15 complete swings in a time of 75 seconds. From this measurement she calculates the acceleration due to gravity on the Moon. What is her result?

Problem 8RQ How do frequency and period relate to each other?

Problem 9E What happens to the wavelength of a wave when the frequency decreases?

Problem 9RQ In one word, what is it chat moves from source to receiver in wave motion?

If the speed of a wave doubles while the frequency remains the same, what happens to the wavelength?

Does the medium in which a wave travels move with the wave? Give examples to support your answer.

Problem 11RQ What is the relationship among frequency, wavelength, and wave speed?

Problem 11E If the speed of a wave doubles while the wavelength remains the same, what happens to the frequency?

Problem 12E You use a vice to firmly clamp one end of a hacksaw blade. You twang the free end and it vibrates. If you do the same, but first place a wad of clay on the free end, how, if at all, will the frequency of vibration differ? Would it make a difference if the wad of clay were stuck to the middle? Explain. (Why could this question have been asked back in Chapter 8?)

Problem 12RQ In what direction are the vibrations relative to the direction of wave travel in a transverse wave?

Problem 13E The needle of a sewing machine moves up and down in simple harmonic motion. Its driving force comes from a rotating wheel that is powered by an electric motor. How do you suppose the period of the up-and-down needle compares with the period of the rotating wheel?

Problem 13RQ In what direction are the vibrations relative to the direction of wave travel in a longitudinal wave?

If you shake the end of a spring to produce a wave, how does the frequency of the wave compare with the frequency of your shaking hand? Does your answer depend on whether you’re producing a transverse wave or a longitudinal wave? Defend your answer.

Problem 14RQ The wavelength of a transverse wave is the distance between successive crests (or troughs). What is the wavelength of a longitudinal wave?

What kind of motion should you impart to the nozzle of a garden hose so that the resulting stream of water approximates a sine curve?

What is meant by the superposition principle?

Problem 16E What kind of motion should you impart to a stretched coiled spring (or Slinky) to provide a transverse wave? To provide a longitudinal wave?

Problem 16RQ Distinguish between constructive interference and destructive interference.

Solution 17E What kind of wave is each of the following? (a) An ocean wave rolling toward Waikiki Beach. (b) The sound of one whale calling another whale underwater. (c) A pulse sent down a stretched rope by snapping one end of it.

Problem 17RQ What kinds of waves can show interference?

Problem 18E If a gas tap is turned on for a few seconds, someone a couple of meters away will hear the gas escaping long before she smells it. What does this indicate about the speed of sound and the speed at which molecules diffuse through the sound-carrying medium?

Problem 18RQ What is a node? What is an antinode?

Problem 19E If we double the frequency of a vibrating object or the wave it produces, what happens to the period?

Problem 19RQ If we double the frequency of a vibrating object or the wave it produces, what happens to the period?

Problem 20E Do the two terms wave speed and wave frequency refer to the same thing? Defend your answer.

Problem 20RQ In the Doppler effect, does frequency change? Does wavelength change? Does wave speed change?

Problem 21E Red light has a longer wavelength than violet light. Which has the greater frequency?

Problem 21RQ Can the Doppler effect be observed with longitudinal waves, with transverse waves, or with both?

Problem 22E What is the frequency of the second hand of a clock? The minute hand? The hour hand?

Problem 23E Consider a wave traveling along a thick rope tied to a thin rope. Which of these three wave characteristics does not undergo change—speed, frequency, or wavelength?

Problem 23RQ How fast must a bug swim to keep up with the waves it produces? How fast must it move to produce a bow wave?

Problem 24E How fast must a bug swim to keep up with the waves it produces? How fast must it move to produce a bow wave?

Problem 24RQ How fast does a supersonic aircraft fly compared with the speed of sound?

Problem 25E How does the frequency of vibration of a small object floating in water compare with the number of waves passing it each second?

Problem 25RQ How does the V shape of a bow wave depend on the speed of the source?

Problem 26E In terms of wavelength, show how far a wave travels in one period.

A bow wave on the surface of water is two-dimensional. How about a shock wave in air?

Problem 27E What is the source of mechanical waves and of electromagnetic waves?

Problem 27RQ True or false: A sonic boom occurs only when an aircraft is breaking through the sound barrier. Defend your answer.

Problem 28E How many nodes, not including the endpoints, are there in a standing wave that is two wavelengths long? Three wavelengths long?

Problem 28RQ True or false: In order for an object to produce a sonic boom, it must be “noisy.” Give two examples to support your answer.

The wave patterns seen in Figures 19.4 and 19.5 are composed of circles. What does this tell you about the speed of waves moving in different directions?

Problem 31E Why is lightning seen before thunder is heard?

Problem 32E A banjo player plucks the middle of a string pinned down at both ends. Where are the nodes of the standing wave in the string? What is the wavelength of the vibrating string?

Problem 33E Violinists sometimes bow a string to produce maximum vibration (antinodes) at one-quarter and three-quarters of the string length rather than at the middle of the string. Then the string vibrates with a wavelength equal to the string length rather than twice the string length. (See Figures 19.13a and b). What is the effect on frequency when this occurs?

Problem 34E A bat chirps as it flies toward a wall. Is the frequency of the echoed chirps it receives higher, lower, or the same as the emitted ones?

Problem 35E A railroad locomotive is at rest with its whistle shrieking, then starts moving toward you. (a) Does the frequency of sound that you hear increase decrease or stay the same? (b) How about the wavelength reaching your ear? (c) How about the speed of sound in the air between you and the locomotive?

Problem 36E Why is there a Doppler effect when the source of sound is stationary and the listener is in motion? In which direction should the listener move to hear a higher frequency? A lower frequency?

Problem 37E When you blow your horn while driving toward a stationary listener, the listener hears an increase in frequency of the horn. Would the listener hear an increase in horn frequency if he or she were also in a car traveling at the same speed in the same direction as you are? Explain.

Problem 38E Is there an appreciable Doppler effect when the motion of the source is at right angles to a listener? Explain.

Problem 39E How does the Doppler effect aid police in detecting speeding motorists?

Problem 40E Astronomers find that light emitted by a particular element at one edge of the Sun has a slightly higher frequency than light from that element at the opposite edge. What do these measurements tell us about the Sun’s motion?

Problem 41E Would it be correct to say that the Doppler effect is the apparent change in the speed of a wave due to motion of the source? (Why is this question a test of reading comprehension as well as a test of physics knowledge?)

Problem 42E How does the phenomenon of interference play a role in the production of bow waves or shock waves?

Problem 43E What can you say about the speed of a boat that makes a bow wave?

Problem 44E Does the conical angle of a shock wave open wider, narrow down, or remain constant as a supersonic aircraft increases its speed?

Problem 45E If the sound of an airplane does not come from the part of the sky where the plane is seen, does this imply that the airplane is traveling faster than the speed of sound? Explain.

Problem 46E Does a sonic boom occur at the moment when an aircraft exceeds the speed of sound? Explain.

Problem 47E Why is it that a subsonic aircraft, no matter how loud it may be, cannot produce a sonic boom?

Imagine a superfast fish that is able to swim faster than the speed of sound in water. Would such a fish produce a “sonic boom”?

Problem 49E Make up a multiple-choice question that would check a classmate’s understanding of the distinction between a transverse wave and a longitudinal wave.

Problem 50E Make up two multiple-choice questions that would check a classmate’s understanding of any of the terms that describe a wave.

Problem 22RQ What is meant by a blue shift and a red shift for light?

Problem 29E A rock is dropped in water, and waves spread over the flat surface of the water. What becomes of the energy in these waves when they die out?.