?Imagine an old hermit living in a cave in the mountains. Just before going to sleep, he

What is the source of all waves?

Distinguish between these parts of a wave: period, amplitude, wavelength, and frequency.

How are frequency and period related to each other?

In one word, what is it that moves from the source to receive in a wave motion?

Does the medium in which a wave travels move with the wave?

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

In what direction are the vibrations in a transverse wave, relative to the direction of wave travel? In a longitudinal wave?

In what direction do compressed regions and rarefied regions of a longitudinal wave travel?

Does sound travel faster in warm air or in cold air? Defend your answer.

How does the speed of sound in water compare with the speed of sound in air? How does the speed of sound in steel compare with the speed of sound in air?

What is the law of reflection for sound?

What is reverberation?

Relate wave speed and bending to the phenomenon of refraction.

Does sound tend to bend upward or downward when it travels faster near the ground than higher up?

How do dolphins perceive their environment in dark and murky water?

Why does a struck tuning fork sound louder when its handle is held against a table?

Distinguish between forced vibrations and resonance.

When you listen to a radio, why do you hear only one station instead of multiple stations at once?

Why do troops “break step” when crossing a bridge?

What kinds of waves exhibit interference?

Distinguish between constructive interference and destructive interference.

What does it mean to say that one wave is out of phase with another?

What physical phenomenon underlies beats?

What is a node? What is an antinode?

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

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

How do the speed of a wave source and the speed of the waves themselves compare when a wave barrier is being produced? How do they compare when a bow wave is being produced?

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

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

Distinguish between a musical sound and noise

Tie a rubber tube, a spring, or a rope to a fixed support and shake it to produce standing waves. See how many nodes you can produce.

Test to see which of your ears has better hearing by covering one ear and finding how far away your open ear can hear the ticking of a clock; repeat for the other ear. Notice also how the sensitivity of your hearing improves when you cup your hands behind your ears.

At the risk of getting your floor wet, slide back and forth in your bathtub at different frequencies and see how the amplitude of the sloshing waves quickly builds up when you slide in rhythm with the waves. (This is best done when you’re alone in the tub.)

Do the activity suggested in Figure 10.24 with a stereo sound system. Simply reverse the wire inputs to one of the speakers so that the two are out of phase. When monaural sound is played and the speakers are brought face to face, the lowering of volume is truly amazing! If the speakers are well insulated, you hear almost no sound at all.

For this activity, you’ll need an isolated loudspeaker (bare of its casing) and a sheet of plywood or cardboard—the bigger the better. Cut a hole about the size of the speaker in the middle of the sheet. Listen to music from the isolated speaker, and then hear the difference when the speaker is placed against the hole. The sheet diminishes the amount of sound from the back of the speaker that interferes with sound coming from the front side, producing a much fuller sound. Now you know why speakers are mounted in enclosures.

Wet your finger and slowly rub it around the rim of a thin-rimmed, stemmed glass while you hold the base of the glass firmly to a tabletop with your other hand. The friction of your finger excites standing waves in the glass, much like the wave made on the strings of a violin by the friction from a violin bow. Try it with a metal bowl.

Swing a buzzer of any kind over your head in a circle. You won’t hear the Doppler shift, but your friends off to the side will. The pitch will increase as the buzzer approaches them and decrease when it recedes. Then switch places with a friend so you can hear it too.

Make the lowest-pitched vocal sound you are capable of; then raise the pitch by singing up the scale to see how many octaves your voice can span. Each octave increase doubles frequency. Compare your number of octaves with those of your friends.

Blow over the top of two empty bottles and see whether the tones produced are of the same pitch. Then put one in a freezer and try the procedure again. Sound travels more slowly in the denser air of the cold bottle, so the note is lower. Try it and see.

\(\text { Frequency }=\frac{1}{\text { period }}\) A pendulum swings to and fro every 3 seconds. Show that its frequency of swing is 1/3 Hz. Text Transcription: Frequency = 1/period

\(\text { Period }=\frac{1}{\text { frequency }}\) Another pendulum swings to and fro at a regular rate of 2 times per second. Show that its period is 0.5 s. Text Transcription: Period = 1/frequency

Wave speed = frequency x wavelength = \(=f \lambda\) A wave 3 m long oscillates 1.5 times each second. Show that the speed of the wave is 4.5 m/s. Text transcription: f lambda

Show that a certain wave with a 1.2-m wavelength and a frequency of 2.5 Hz has a wave speed of 3.0 m/s.

A tuning fork produces a sound with a frequency of 256 Hz and a wavelength in air of 1.33 m. Show that the speed of sound in the vicinity of the fork is 340 m/s.

A nurse approaches his patient and counts 72 heartbeats in 1 min. Show that the frequency and period of the heartbeats are 1.2 Hz and 0.83 s, respectively.

A weight suspended from a spring is seen to bob up and down over a distance of 20 cm twice each second. (a) What is its frequency? (b) What is its period? (c) What is its amplitude?

We know that speed v = distance/time. Show that when the distance traveled is one wavelength l and the time of travel is the period T (which equals 1/frequency) you get \(v=f \lambda\). Text Transcription: F lambda

A skipper on a boat 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. (a) Show that his estimation of wave speed is 3 m/s by the classic formula for speed, distance divided by time. (b) Show that his estimation of wave speed is 3 m/s by frequency × wavelength.

A mosquito flaps its wings at the rate of 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.

The highest-frequency sound humans can hear is about 20,000 Hz. What is the wavelength of sound in air at this frequency? What is the wavelength of the lowest-frequency sound we can hear, about 20 Hz?

Microwave ovens typically cook food using microwaves with frequency of about 3 GHz (1 gigahertz = 109 Hz). Show that the wavelength of these microwaves traveling at the speed of light is 10 cm.

For years, marine scientists were mystified by sound waves detected by underwater microphones in the Pacific Ocean. These so-called T waves were among the purest sounds in nature. Eventually the researchers traced the source to underwater volcanoes whose rising columns of bubbles resonated like organ pipes. A typical T wave has a frequency of 7 Hz. Knowing that the speed of sound in seawater is 1530 m/s, show that the wavelength of a T wave is 219 m.

An oceanic depth-sounding vessel surveys the ocean bottom with ultrasonic waves that travel 1530 m/s in seawater. Show that when the time delay of an echo to the ocean floor below is 4 s, the depth of the water is 3060 m.

A bat flying in a cave emits a sound and receives its echo 0.1 s later. Show that the distance to the wall of the cave is 17 m.

Susie hammers on a block of wood 85 m from a large brick wall. Each time she hits the block, she hears an echo 0.5 s later. With this information, show that the speed of sound is 340 m/s.

Imagine an old hermit living in a cave in the mountains. Just before going to sleep, he yells “WAKE UP!” The sound echoes off the nearest mountain and returns 8 hours later. Show that the mountain is almost 5000 km distant.

On a piano keyboard, you strike middle C, of frequency 262 Hz. (a) Show that the period of one vibration of this tone is 0.004 s. (b) Show that as the sound leaves the instrument at a speed of 340 m/s, its wavelength in air is 1.33 m.

(a) Say you were foolish enough to play your keyboard instrument under water, where the speed of sound is 1500 m/s. (a) Show that the wavelength of the middle-C tone would be 5.86 m. (b) Explain why middle C (or any other tone) has a longer wavelength in water than in air.

A beat frequency is equal to the difference between a pair of sound frequencies. What beat frequencies are possible with tuning forks of frequencies 256, 259, and 261 Hz?

As shown in the drawing, the half-angle of the shockwave cone generated by a supersonic aircraft is \(45^{\circ}\). What is the speed of the plane relative to the speed of sound? Text Transcription: 45 degree

All the waves shown have the same speed in the same medium. Use a ruler and rank these waves, from greatest to least, in terms of first the wave amplitude, next the wavelength, then the frequency, and finally the period.

Four different pairs of transverse wave pulses move toward each other. At some point in time, the pulses meet and interact (interfere) with each other. Rank the four pairs, from most to least, on the basis of distance from equilibrium that results when the centers of the pulses coincide.

Rank, from highest to lowest, the pitch heard when a fire engine is traveling: (a) toward the listener at 30 km/h, (b) toward the listener at 50 km/h, and (c) away from the listener at 20 km/h.

The following three shock waves are produced by supersonic aircraft. Rank their speeds from greatest to least.

Rank, from greatest to least, the speed of sound through: (a) air (b) steel (c) water.

Rank the beat frequencies, from highest to lowest, for the following pairs of sounds: (a) 132 Hz, 136 Hz; (b) 264 Hz, 258 Hz; (c) 528 Hz, 531 Hz; (d) 1056 Hz, 1058 Hz.

Phil Physiker blows across the mouths of identical containers A, B, and C with different amounts of water, as shown. Rank, from highest to lowest, the pitches of the resulting sounds. Try it and hear!

A student that you’re tutoring says that the terms wave speed and wave frequency refer to the same thing. What is your response?

You dip your finger at a steady rate into a puddle of water to make waves. What happens to the wavelength if you dip your finger more frequently?

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

When sound becomes louder, which wave characteristic is probably increasing: frequency, wavelength, amplitude, or speed?

What two physics mistakes occur in a science-fiction movie that shows, in outer space, a distant explosion that you see and hear at the same time?

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

A friend says that wave speed is equal to the frequency of a wave times its wavelength, and another says it’s equal to wavelength divided by the period of the wave. Which friend do you agree with?

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 kind of motion should you impart to a stretched, coiled spring (or to a Slinky) to produce a transverse wave? A longitudinal wave?

A cat can hear sound frequencies up to 70,000 Hz. Bats send and receive ultra-high-frequency squeaks up to 120,000 Hz. Which animal hears sound of shorter wavelengths: cats or bats?

The sounds emitted by bats are extremely intense. Why cannot humans hear them?

Why do you not hear the sound of a distant fireworks display until after you see it?

If the Moon blew up, why would we not hear the sound?

Why would it be futile to attempt to detect sounds from other planets with the use of state-of-the-art audio detectors?

A pair of sound waves of different wavelengths reach the listener’s ear as shown. Which has the higher pitch: the short-wavelength sound or the long-wavelength sound?

In Olympic competition, the sound of the starter’s gun is picked up by a microphone and sent electronically to speakers at every runner’s starting block. Why?

A friend says that sound travels faster in warm air than in cooler air. Do you agree or disagree?

Why does your voice sound fuller when you are singing in the shower?

A bat chirps as it flies toward a wall. Is the frequency of the echoed chirps it receives higher, lower, or the same as that of the emitted chirps? A B C

A friend says that refraction of any kind of wave is due to a change in wave speed. Do you agree or disagree?

Why are marchers following a band at the end of a long parade out of step with marchers near the front?

What is the danger posed by people in the balcony of an auditorium stamping their feet in a steady rhythm?

Why is the sound of a harp soft compared with the sound of a piano?

What physics principle does Manuel use when he pumps in rhythm with the natural frequency of the swing?

How can a certain note sung by a singer cause a crystal glass to shatter?

A nylon guitar string vibrates in a standing-wave pattern, as shown. What is the wavelength of the wave?

Two bunnies hop at slightly different rates but remain side by side. The first takes 50 hops per minute and the other takes 48 hops per minute. If they begin hopping together, when will they again be “in step”?

Suppose a piano tuner hears three beats per second when listening to the combined sound from his tuning fork and the piano note being tuned. After slightly tightening the string, he hears five beats per second. Should the string now be tightened further or loosened?

When the frequency of sound is doubled, what change occurs in its speed? What change occurs in its wavelength? Defend your answers.

A railroad locomotive is at rest with its whistle shrieking, and then it starts moving toward you. (a) Does the frequency of the 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?

When you blow your horn while driving toward a stationary listener, she hears an increase in pitch of the horn. Would the listener hear an increase in the pitch of sound emitted by the horn if she were also in a car traveling at the same speed in the same direction as you are? Explain.

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

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

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?)

A swimming duck produces a bow wave attached to the duck. a) Is the duck swimming faster than water wave speed? (b) Does the angle of the bow wave open wider, narrow down, or remain constant as the duck increases its speed?

Does the conical angle of a shock wave become wider, narrower, or remain constant as a supersonic aircraft increases its speed?

If the sound of an airplane does not originate in 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.

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

Distinguish between noise and music in terms of the vibrations produced.

If the fundamental frequency of a guitar string is 220 Hz, what is the frequency of the second harmonic? Of the third harmonic?

How many nodes, excluding end points, are in a standing wave that is three wavelengths long? In a standing wave that is four wavelengths long?

Which of the two musical notes displayed individually on an oscilloscope screen has the higher pitch? Which indicates the louder sound?

What characteristic of sound distinguishes a piano from a guitar?

What does it mean to say that a radio station is “at 101.1 on your FM dial”?

At the instant that a high-pressure region is created just outside the prongs of a vibrating tuning fork, what is being created inside, between the prongs?

If a bell is ringing inside a bell jar, we can no longer hear it when the air is pumped out, but we can still see the bell. Discuss the differences between the properties of sound and light that this indicates.

If the speed of sound depended on its frequency, why would you not enjoy a concert sitting far from the stage, say in the second balcony.

Why is the Moon described as a “silent planet”?

Discuss why sound travels faster in moist air. Relate this to the fact that at the same temperature, water-vapor molecules have the same average kinetic energy as the heavier nitrogen and oxygen molecules in the air. Continue your discussion about the average speeds of \(\mathrm{H}_{2} \mathrm{O}\) molecules compared with those of \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\) molecules. Text Transcription: H_2O N_2 O_2

Why is an echo weaker than the original sound? Discuss the role of distance.

One rule of thumb for estimating the distance in kilometers between an observer and a lightning stroke is to divide the number of seconds in the interval between the flash and the sound by 3. Discuss whether or not this rule is correct.

If a single disturbance at an unknown distance away sends out both transverse and longitudinal waves that travel with distinctly different speeds in the medium, such as in the ground during an earthquake, discuss how the distance to the disturbance is determined.

As you pour water into a glass, you repeatedly tap the glass exterior with a spoon. As the tapped glass is being filled, does the pitch of the sound increase or decrease? (What should you do to answer this question?)

Physics instructor Peter Hopkinson delights in bringing physics into social situations. When dining out with friends, he produces resonance in an empty wine glass by rubbing his wetted fingers on its rim. While all listen to the resonating sound, he asks how the sound frequency will be affected when wine or water is poured into the glass. What is your answer?

What physics principle is used in radar guns to find the speeds of tennis balls and baseballs at sporting events?

A special device can transmit sound that is out of phase with the sound of a noisy jackhammer to the jackhammer operator by means of earphones. Over the noise of the jackhammer, the operator can easily hear your voice, even though you are unable to hear his. Explain.

Two sound waves of the same frequency can interfere with each other, but two sound waves must have different frequencies in order to make beats. Discuss the reason for this.

Discuss whether or not a sonic boom occurs at the moment when an aircraft exceeds the speed of sound.