sound final ch.12

You stand a certain distance away from a speaker and you hear a certain intensity of sound. If you double your distance from the speaker, what happens to the sound intensity at your new position?

drops to 1/4 its original value For a source of a given power P, the intensity is given by I = P/4pr2. So if the distance doubles, the intensity must decrease to one-quarter its original value.

When a sound wave passes from air into water, what properties of the wave will change?

Both wave velocity and wavelength Wave speed must change (different medium). Frequency does not change (determined by the source). Now, v = fl and since v has changed and f is constant then l must also change.

If you blow across the opening of a partially filled soda bottle, you hear a tone. If you take a big sip of soda and then blow across the opening again, how will the frequency of the tone change?

Frequency will decrease By drinking some of the soda, you have effectively increased the length of the air column in the bottle. A longer pipe means that the standing wave in the bottle would have a longer wavelength. Since the wave speed remains the same, and since we know that v = f l, then we see that the frequency has to be lower.

In the previous question, the horn had a rest frequency of f0, and we found that your friend heard a higher frequency f1 due to the Doppler shift. The sound from the boat hits the cliff behind your friend and returns to you as an echo. What is the frequency of the echo that you hear?

Higher than F1 The sound wave bouncing off the cliff has the same frequency f1 as the one hitting the cliff (what your friend hears). For the echo, you are now a moving observer approaching the sound wave of frequency f1 so you will hear an even higher frequency.

You are heading toward an island in a speedboat and you see your friend standing on the shore, at the base of a cliff. You sound the boat's horn to alert your friend of your arrival. If the horn has a rest frequency of f0, what frequency does your friend hear?

Higher than f0 Due to the approach of the source toward the stationary observer, the frequency is shifted higher. This is the same situation as depicted in the previous question.

Do sound waves travel faster in water or in ice?

ICE Speed of sound depends on the inertia of the medium and the restoring force. Since ice and water both consist of water molecules, the inertia is the same for both. However, the force holding the molecules together is greater in ice (because it is a solid), so the restoring force is greater. Since v = sqroot(force / inertia), the speed of sound must be greater in ice !

Speakers A and B emit sound waves of l = 1 m, which interfere constructively at a donkey located far away (say, 200 m). What happens to the sound intensity if speaker A steps back 2.5 m?

Intensity goes to ZERO If l = 1 m, then a shift of 2.5 m corresponds to 2.5l, which puts the two waves out of phase, leading to destructive interference. The sound intensity will therefore go to zero.

Intensity level is given by b = 10 log(I/I0) with I0 = 10-12 W/m2. The usual threshold of human hearing is defined as intensity level of b = 0 dB. What does this actually mean in terms of sound intensity?

Intensity is 1.0W/m^2 In order for b to be equal to zero, the term log(I/I0) must also be zero. This occurs when the argument is 1.0, because log(1.0) = 0. In other words, the value of I must be equal to I0.

We just determined that the wavelength of the sound wave will change when it passes from air into water. How will the wavelength change?

It will increase The speed of sound is greater in water, because the force holding the molecules together is greater. This is generally true for liquids, as compared to gases. If the speed is greater and the frequency has not changed (determined by the source), then the wavelength must also have increased v = f(wavelength).

Do you expect an echo to return to you more quickly or less quickly on a hot day, as compared to a cold day?

On a hot day The speed of sound in a gas increases with temperature. This is because the molecules are bumping into each other faster and more often, so it is easier to propagate the compression wave (sound wave).

You have a long pipe and a short pipe. Which one has the higher frequency?

Short pipe A shorter pipe means that the standing wave in the pipe would have a shorter wavelength. Since the wave speed remains the same, the frequency has to be higher in the short pipe.

When you tune a guitar string, what physical characteristic of the string are you actually changing?

The tension in the string By tightening (or loosening) the knobs on the neck of the guitar, you are changing the tension in the string. This alters the wave speed, and therefore alters the frequency of the fundamental standing wave because f = v/2L .

You blow into an open pipe and produce a tone. What happens to the frequency of the tone if you close the end of the pipe and blow into it again?

You hear a lower frequency In the open pipe, 1/2 of a wave "fits" into the pipe, while in the closed pipe, only 1/4 of a wave fits. Because the wavelength is larger in the closed pipe, the frequency will be lower.

A quiet radio has an intensity level of about 40 dB. Busy street traffic has a level of about 70 dB. How much greater is the intensity of the street traffic compared to the radio?

about 1000 times increase by 10 dB --> increase intensity by factor of 101 (10) increase by 20 dB --> increase intensity by factor of 102 (100) increase by 30 dB --> increase intensity by factor of 103 (1000)

You hear a fire truck with a certain intensity, and you are about 1 mile away. Another person hears the same fire truck with an intensity that is about 10 times less. Roughly how far is the other person from the fire truck?

about 3 miles Remember that intensity drops with the inverse square of the distance, so if intensity drops by a factor of 10, the other person must be 10 farther away, which is about a factor of 3

You drop a rock into a well, and you hear the splash 1.5 s later. If the depth of the well were doubled, how long after you drop the rock would you hear the splash in this case?

between 1.5 s and 3 s later Since the speed of sound is so much faster than the speed of the falling rock, we can essentially ignore the travel time of the sound. As for the falling rock, it is accelerating as it falls, so it covers the bottom half of the deeper well much quicker than the top half. The total time will not be exactly 3 s, but somewhat less.

When Mary talks, she creates an intensity level of 60 dB at your location. Alice talks with the same volume, also giving 60 dB at your location. If both Mary and Alice talk simultaneously from the same spot, what would be the new intensity level that you hear?

between 60-120dB Recall that a difference of 10 dB in intensity level b corresponds to a factor of 101 in intensity. Similarly, a difference of 60 dB in b corresponds to a factor of 106 in intensity!! In this case, with two voices adding up, the intensity increases by only a factor of 2, meaning that the intensity level is higher by an amount equal to: Db = 10 log(2) = 3 dB. The new intensity level is b = 63 dB.

Observers A, B, and C listen to a moving source of sound. The location of the wave fronts of the moving source with respect to the observers is shown below. Which of the following is true?

frequency is highest at point c The number of wave fronts hitting observer C per unit time is greatest - thus the observed frequency is highest there

A wood whistle has a variable length. You just heard the tone from the whistle at maximum length. If the air column is made shorter by moving the end stop, what happens to the frequency?

frequency will increase A shorter pipe means that the standing wave in the pipe would have a shorter wavelength. Since the wave speed remains the same, and since we know that v = f l, then we see that the frequency has to increase when the pipe is made shorter.

The traces below show beats that occur when two different pairs of waves interfere. For which case is the difference in frequency of the original waves greater?

pair 1 Recall that the beat frequency is the difference in frequency between the two waves: fbeat = f2 - f1 Pair 1 has the greater beat frequency (more oscillations in same time period), so Pair 1 has the greater frequency difference.

If you fill your lungs with helium and then try talking, you sound like Donald Duck. What conclusion can you reach about the speed of sound in helium?

speed of sound is greater in helium The higher pitch implies a higher frequency. In turn, since v = fl, this means that the speed of the wave has increased (as long as the wavelength, determined by the length of the vocal chords, remains constant).