Q: A flute can be modeled as a pipe open at both ends. If the length of the flute is $$0.66 m$$, what is the fundamental frequency produced, assuming the speed of sound in air is $$343 m/s$$?

$$f_1$$ = \frac{343}{2 \times 0.66}$$

Question 1

Which of the following best describes the type of wave produced when a piston moves in and out in a long air-filled pipe, as shown in the first image?

Accepted Answer

A longitudinal wave, because the air molecules move parallel to the direction of wave propagation.

Question 2

The speed of sound in a medium is given by $$v = \sqrt{\frac{B}{\rho}}. If $$the bulk modulus $$B of a $$material increases while its density $$\rho$$ remains constant, what happens to the speed of sound?

Accepted Answer

The speed of sound increases.

Question 3

A sound wave in air is described by the displacement function $$s(x, t) = s_m \cos(kx - \omega t). $$What does $$s_m$$ represent in this equation?

Accepted Answer

The displacement amplitude, or the maximum displacement of an air element from equilibrium.

Question 4

In the context of sound waves, what is the relationship between the pressure amplitude $$\Delta p_m$$ and the displacement amplitude $$s_m$$?

Accepted Answer

$$\Delta p_m = (v \rho \omega) s_m$$

Question 5

Two sound sources $$S_1$$ and $$S_2$$ emit waves in phase and are separated by a distance $$D = 1.5 \lambda. At a $$point $$P_2$$ directly in line with the sources, the path difference is $$D. $$What type of interference occurs at $$P_2$$?

Accepted Answer

Fully destructive interference

Question 6

The intensity $$I of a $$sound wave from a point source at a distance $$r is $$given by $$I = \frac{P_{avg}}{4 \pi r^2$}. If $$the distance from the source is doubled, what happens to the intensity?

Accepted Answer

It is reduced to one-fourth its original value.

Question 7

The sound level $$\beta in $$decibels is defined as $$\beta = (10 	ext{ dB}) \log_{10} \left( \frac{I}{I_0$} ight). If $$the intensity increases by a factor of 100, by how many decibels does the sound level increase?

Accepted Answer

20 dB

Question 8

For a pipe open at both ends with length $$L$$, what is the wavelength $$\lambda of $$the fundamental (first harmonic) standing wave?

Accepted Answer

$$\lambda = 2L$$

Question 9

A pipe closed at one end and open at the other has length $$L. $$Which of the following is the correct expression for the wavelength of the $$nth $$harmonic (where $$n is an $$odd integer)?

Accepted Answer

$$\lambda = 4L/n$$

Question 10

Two sound waves of nearly equal frequencies $$f_1$$ and $$f_2$$ interfere at a point, producing beats. What is the beat frequency observed?

Accepted Answer

$$|f_1$ - f_2$|$$

Question 11

A sound source emits a frequency $$f$$ and moves toward a stationary observer with speed $$v_S. $$The speed of sound in air is $$v. $$What is the frequency $$f'$$ detected by the observer?

Accepted Answer

$$f' = f \frac{v}{v - v_S}$$

Question 12

A submarine emits a sonar signal of frequency $$f = 1000 Hz in $$water where the speed of sound is $$v = 5470 km/h. If $$the submarine moves toward a stationary detector at $$v_S = 45 km/h$$, what is the detected frequency $$f'$$?

Accepted Answer

$$f' = 1000 \frac{5470}{5470 - 45}$$

Question 13

Which of the following statements about the displacement and pressure variation graphs for a sound wave is correct?

Accepted Answer

The displacement is maximum when the pressure variation is zero.

Question 14

If the frequency of a sound wave is doubled while its speed remains constant, what happens to its wavelength?

Accepted Answer

It is halved.

Question 15

A point source emits sound waves isotropically. If the power output of the source is $$P_{avg}$$, what is the intensity at a distance $$r$$ from the source?

Accepted Answer

$$I = \frac{P_{avg}}{4 \pi r^2$}$$

Question 16

Which of the following best explains why the speed of sound is greater in steel than in air?

Accepted Answer

Steel has a much higher bulk modulus than air.

Question 17

A flute can be modeled as a pipe open at both ends. If the length of the flute is $$0.66 m$$, what is the fundamental frequency produced, assuming the speed of sound in air is $$343 m/s$$?

Accepted Answer

$$f_1$$ = \frac{343}{2 	imes 0.66}$$

Question 18

If two sound waves of equal amplitude and slightly different frequencies are played together, what phenomenon is observed and what is its cause?

Accepted Answer

Beats, due to interference between the two waves.

Question 19

A detector moves toward a stationary sound source with speed $$v_D. $$What is the detected frequency $$f'$$?

Accepted Answer

$$f' = f \frac{v + v_D}{v}$$

Study Notes: Sound Waves and Their Properties

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