Based on the information presented in the introduction of this problem, what is a sound wave?

1HW 7 SolutionsWhat Is a Sound Wave?a)Based on the information presented in the introduction of this problem, what is a sound wave?Propagation of pressure fluctuations in a mediumb)Having established that a sound wavecorresponds to pressure fluctuations in themedium, what can you conclude about thedirection in which such pressure fluctuationstravel?Pressure fluctuations travel along thedirection of propagation of the soundwave.c)Does air play a role in the propagation of the human voice from one end of a lecture hall tothe other?Yes.d)The graphs shown in Fig.1represent pressure variation versus time recorded by amicrophone. Which could correspond to a sound wave?Enter the letters of all the correct answers in alphabetical order. Do not use commas. Forexample, if you think all three graphs could represent sound waves, enterABC.BCe)Figure 2shows a sound wave consistingof a sinusoidal displacement of air particlesversus time, as recorded at a fixed location.For sinusoidal waves, it is possible toidentifyaspecificfrequency(rateofoscillation) and wavelength (distance inspace corresponding to one complete cycle).Taking the speed of sound in air to be 344 m/s, what are the frequencyfand the wavelengthλofthe sound wave shown in the graph?Express your answers in, respectively, hertz and meters tothree significant figures. Separate the two answers with a comma.1000Hz,0.344 mf)A certain sound is recorded by a microphone. The same microphone then detects a secondsound, which is identical to the first one except that the amplitude of the pressure fluctuations islarger. In addition to the larger amplitude, what distinguishes the second sound from the firstone?It is perceived as louder.g)A certain sound is recorded by a microphone. A second sound that has twice the frequency isdetected by the same microphone. In addition to the higher frequency, what distinguishes thesecond sound from the first one?It is perceived as higher in pitch.When we double thefrequency of a sound wave, we produce a sound that is said to be anoctaveabove the first.

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Part A = Propagation of pressure fluctuations in a medium Part B = Pressure fluctuations travel along the direction of propagation of the sound wave. Part C = yes Part D = BC

Part E = 1000,0.344

Part F = It is perceived as louder. Part G = It is perceived as higher in pitch. Part H = the harmonic content

Solutions Below:

Learning Goal: To understand the nature of a sound wave, including its properties: frequency, wavelength, loudness, pitch, and timbre. Sound is a phenomenon that we experience constantly in our everyday life. Therefore, it is important to understand the physical nature of a sound wave and its properties to correct common misconceptions about sound propagation. Most generally, a sound wave is a longitudinal wave that propagates in a medium (i.e., air). The particles in the medium oscillate back and forth along the direction of motion of the wave. This displacement of the particles generates a sequence of compressions and rarefactions of the medium. Thus, a sound wave can also be described in terms of pressure variations that travel through the medium. The pressure fluctuates at the same frequency with which the particles’ positions oscillate.

When the human ear perceives sound, it recognizes a series of pressure fluctuations rather than displacements of individual air particles.

Part A

Based on the information presented in the introduction of this problem, what is a sound wave? A. Propagation of sound particles that are different from the particles that comprise the medium B. Propagation of energy that does not require a medium C. Propagation of pressure fluctuations in a medium D. Propagation of energy that passes through empty spaces between the particles that comprise the medium

C. Propagation of pressure fluctuations in a medium

Part B

Having established that a sound wave corresponds to pressure fluctuations in the medium, what can you conclude about the direction in which such pressure fluctuations travel? A. The direction of motion of pressure fluctuations is independent of the direction of motion of the sound wave. B. Pressure fluctuations travel perpendicularly to the direction of propagation of the sound wave. C. Pressure fluctuations travel along the direction of propagation of the sound wave.

C. Pressure fluctuations travel along the direction of propagation of the sound wave.

Part C

Does air play a role in the propagation of the human voice from one end of a lecture hall to the other? A. yes B. no

A. yes

Part D

The graphs shown here represent pressure variation versus time recorded by a microphone. Which could correspond to a sound wave?

Enter the letters of all the correct answers in alphabetical order. Do not use commas. For example, if you think all three graphs could represent sound waves, enter ABC.

BC

Part E

The next graph shows a sound wave consisting of

a sinusoidal displacement of air particles versus time, as recorded at a fixed location. For sinusoidal waves, it is possible to identify a specific frequency (rate of oscillation) and wavelength (distance in space corresponding to one complete cycle). Taking the speed of sound in air to be 344 m/s, what are the frequency f and the wavelength lambda of the sound wave shown in the graph? Express your answers in, respectively, hertz and meters to three significant figures. Separate the two answers with a comma. The velocity of a wave equals its frequency times the wavelength: v = fλ

V is given as 344m/s and T is shown by the graph to be 10-3s = 0.001s. Since f = 1/T, f = 1/0.001 = 1000Hz

Therefore: v = fλ 344 = 1000λ

λ = 0.344

So the answer is:

1000,0.344

Note: pay attention to the labellings of the axes. For this problem, the x-axis was labeled as t(s), so it’s representing period, not λ

Part F

A certain sound is recorded by a microphone. The same microphone then detects a second sound, which is identical to the first one except that the amplitude of the pressure fluctuations is larger. In addition to the larger amplitude, what distinguishes the second sound from the first one? A. It is perceived as higher in pitch. B. It is perceived as louder. C. It has a higher frequency. D. It has a longer wavelength.

B. It is perceived as louder.

Part G

A certain sound is recorded by a microphone. A second sound that has twice the frequency is detected by the same microphone. In addition to the higher frequency, what distinguishes the second sound from the first one? A. It is perceived as higher in pitch. B. It is perceived as louder. C. It has a higher amplitude. D. It has a longer wavelength.

A. It is perceived as higher in pitch.

Part H

What varies between two tones that are different in timbre, that is, two tones that have the same fundamental frequency but are produced, say, by different musical instruments? Note that Figures (b) and (c) from Part D could represent tones with different timbre. A. the pitch B. the harmonic content C. nothing

B. the harmonic content