Chapter 12: Sound

Two loudspeakers are about 10m apart in the front of a large classroom. If either speaker plays a pure tone at a single frequency of 400 Hz, the loudness seems pretty even as you wander around the room, and gradually decreases in volume as you move farther from the speaker. If both speakers play the same tone together, what do you hear as you wander around the room? a) The pitch of the sound increases to 800 Hz, and the sound is louder but not twice as loud. It is louder closer to the speakers and gradually decreases as you move away from the speakers - except near the back wall, where a slight echo makes the sound louder. b) The sound is louder but maintains the same relative spatial pattern of gradually decreasing volume as you move away from the speakers. c) As you move around the room, some areas seem to be dead spots with very little sound, whereas other spots seem to be louder than with only one speaker. d) The sound is twice as loud- so loud that you cannot hear any difference as you move around the room. e) At points equidistant from both speakers, the sound is twice as loud. In the rest of the room, the sound is the same as if a single speaker were playing.

c (The two speakers create sound waves that interact as described by the principle of superposition. When the waves overlap, the frequency remains the same; it does not double. If the speakers occupied the same location so that each point in the room were equidistant from the speakers, then the intensity would double everywhere. However, the speakers are separated by a distance of 10 m. Since the path lengths from each speaker to different locations around the room are not the same, at some points in the room the path difference will be an odd integer number of half wavelengths, so the sounds will destructively interfere. At other locations in the room the speakers will be equidistant, or the path difference will be an integral number of whole wavelengths, and the sounds will constructively interfere. This results in dead spots and loud spots in the room.)

A guitar string vibrates at a frequency of 330 Hz with wavelength 1.40 m. The frequency and wavelength of this sound in air (20˚C) as it reaches our ears is a) same frequency, same wavelength b) higher frequency, same wavelength c) lower frequency, same wavelength d) same frequency, longer wavelength e) same frequency, shorter wavelength

e (As the string oscillates, it causes the air to vibrate at the same frequency. Therefore, the sound wave will have the same frequency as the guitar string, so answers (b) and (c) are incorrect. The speed of sound in air at 20°C is 343 m/s. The speed of sound in the string is the product of the wavelength and frequency, 462 m/s, so the sound waves in air have a shorter wavelength than the waves on the string.)

A guitar string is vibrating at its fundamental frequency f. Which of the following is not true? a) Each small section of the guitar string oscillates up and down at a frequency f. b) The wavelength of the standing wave on the guitar string is wavelength = v/f, where v is the velocity of the wave on the string. c) A sound wave created by this vibrating string propagates through the air with a frequency f. d) A sound wave created by this vibrating string propagates through the air with wavelength = v/f, where v is the velocity of sound in air. e) The wavelength of the standing wave on the guitar string is wavelength = l, where l is the length of the string.

e (As the string vibrates, each part of the string (other than the nodes) oscillates at the same frequency, so answer (a) is true. This oscillation excites the air to vibrate at that frequency, so answer (c) is true. The wave relationships in answers (b) and (d) are true for any wave, so both are true in this case as well. However, the speed of the wave on the string is determined by the tension and mass of the string, and the speed of sound in the air is determined by the temperature, pressure, and density of the air. The two speeds are not necessarily the same. Since the sound wave and wave on the string have the same frequencies, but not necessarily the same wave speeds, they do not necessarily have the same wavelengths. Thus, (e) is not true.)

In which of the following is the wavelength of the lowest vibration mode the same as the length of the string or tube? a) a string b) an open tube c) a tube closed at one end d) all of the above e) none of the above

e (n a string or open tube the lowest vibration mode is equal to half of a wavelength. In a tube closed at one end the lowest vibration mode is equal to a quarter of a wavelength. Therefore, none of the listed objects have a lowest vibration mode equal to a wavelength.)

You are driving at 75 km/h. Your sister follows in the car behind at 75 km/h. When you honk your horn, your sister hears a frequency a) higher than the frequency you hear b) lower than the frequency you hear c) the same as the frequency you hear d) you cannot tell without knowing the horn's frequency

c (A common misconception is that since the cars are moving there must be a Doppler shift. In this situation, however, there is no relative motion between the two vehicles. The two vehicles travel in the same direction at the same speed. Since the distance between them does not change, you and your sister will hear the horn sound at the same frequency.)

What is the evidence that sound is a form of energy?

Evidence that sound is a form of energy is found in the fact that sound can do work. A sound wave created in one location can cause the mechanical vibration of an object at a different location. For example, sound can set eardrums in motion, make windows rattle, or even shatter a glass. See Fig. 11-19 for a photograph of a goblet shattering from the sound of a trumpet.

What is the evidence that sound travels as a wave?

Sound exhibits several phenomena that give evidence that it is a wave. Interference is a wave phenomenon, and sound produces interference (such as beats). Diffraction is a wave phenomenon, and sound can be diffracted (such as sound being heard around corners). Refraction is a wave phenomenon, and sound exhibits refraction when passing obliquely from one medium to another. Sound also requires a medium, a characteristic of mechanical waves.

Do you expect an echo to return to you more quickly on a hot day or a cold day? a) hot day b) cold day c) same on both days

a (Students may answer that the speed of sound is the same, if they do not understand that the speed of sound is not constant, but depends upon the temperature of the air. When it is hotter, the speed of sound is greater, so it takes less time for the echo to return.)

An organ pipe with a fundamental frequency f is open at both ends. If one end is closed off, the fundamental frequency will a) drop by half b) not change c) double

a (The fundamental wavelength of an open-ended organ pipe is twice the length of the pipe. If one end is closed, then the fundamental wavelength is four times the length of the pipe. Since the wavelength doubles when one end of the pipe is closed off, and the speed of sound remains constant, the fundamental frequency is cut in half.)

A musical note that is two octaves higher than a second note a) has twice the frequency of the second note b) has four times the frequency of the second note c) has twice the amplitude of the second note d) is 3 dB louder than the second note e) none of the above

b (The octave is a measure of musical frequency, not loudness. Raising a note by one octave requires doubling the frequency. Therefore, raising a note by two octaves is doubling the frequency twice, which is the same as quadrupling the frequency.)

A guitar player shortens the length of a guitar's vibrating string by pressing the string straight down onto a fret. The guitar then emits a higher pitched note because a) the string's tension has been dramatically increased b) the string can vibrate with a much larger amplitude c) the string vibrates at a higher frequency

c (Pushing the string straight down onto a fret does not affect the tension a significant amount, due to the fret being so close to the string. The amplitude of the wave is determined by how hard the string is plucked, not by pushing the string onto the frets. When the string is pushed down, its effective length is shortened, which shortens the wavelength and thus increases the oscillation frequency. (The wave speed on the string doesn't change due to fretting the string.))

The sound level near a noisy air conditioner is 70 dB. If two such units operate side by side, the sound level near them would be a) 70 dB b) 73 dB c) 105 dB d) 140 dB

b (A common misconception is to treat the sound intensity level as a linear scale instead of a logarithmic scale. If the sound intensity doubles, the intensity level increases by about 3 dB, so the correct answer is 73 dB.)

Sound waves are a) transverse waves characterized by the displacement of air molecules. b) longitudinal waves characterized by the displacement of air molecules c) longitudinal waves characterized by pressure differences d) both b and c e) a, b, and c

d (Sound waves are longitudinal waves, so (a) is incorrect. The sound waves can be characterized either by the longitudinal displacement of the air molecules or by the pressure differences that cause the displacements.)

When a sound wave passes from air into water, what properties of the wave will change? a) frequency b) wavelength c) wave speed d) both frequency and wavelength e) both wave speed and wavelength

e (A common misconception is that the frequency of a sound changes as it passes from air to water. The frequency is the number of wave crests that pass a certain point per unit time. If this value were to change as it entered the water, then wave crests would build up or be depleted over time. This would make the interface an energy source or sink, which it is not. The speed of sound in water is greater than in air, so the speed of the wave changes. Since the frequency cannot change, the increase in speed results in an increase in wavelength.)

To make a given sound seem twice as loud, how should a musician change the intensity of the sound? a) double the intensity b) halve the intensity c) quadruple the intensity d) quarter the intensity e) increase the intensity by a factor of 10

e (Students often think that the sound intensity is the same as loudness and therefore mistakenly answer that doubling the intensity will double the loudness. However, the ear interprets loudness on a logarithmic scale. For something to sound twice as loud, it must have an intensity that is 10 times as great.)