Q: In a sound wave, the excess pressure at a point is given by $$\Delta P(x, t) = -B \frac{\partial y(x, t)}{\partial x}. If$$ $$y(x, t) = A \cos(kx - \omega t)$$, what is the pressure amplitude $$\Delta P_{\text{max}}$$?

$$\Delta P_{\text{max}} = B k A$$

Q: What is the relationship between intensity $$I$$ and pressure amplitude $$\Delta P_{\text{max}} in a $$sound wave?

$$I \propto \Delta P_{\text{max}}^2$$

Question 1

A sound wave propagates through air with a displacement described by $$y(x, t) = A \sin(kx - \omega t). $$What is the expression for the intensity $$I of $$this sound wave in terms of the displacement amplitude $$A$$?

Accepted Answer

$$I = \frac{1}{2} \$$omega^2$$ A^2$ \rho v$$

Question 2

In a sound wave, the excess pressure at a point is given by $$\Delta P(x, t) = -B \frac{\partial y(x, t)}{\partial x}. If$$ $$y(x, t) = A \cos(kx - \omega t)$$, what is the pressure amplitude $$\Delta P_{	ext{max}}$$?

Accepted Answer

$$\Delta P_{	ext{max}} = B k A$$

Question 3

A tube is closed at one end and open at the other. What is the fundamental frequency $$f_1 of a $$standing sound wave in this tube of length $$L$$ and speed of sound $$v$$?

Accepted Answer

$$f_1$$ = \frac{v}{4L}$$

Question 4

The intensity of a sound wave is measured to be $$20 dB at a $$distance of $$15 m $$from the source. How close should you move to the source for the sound level to be $$60 dB$$?

Accepted Answer

$$0.15 m$$

Question 5

Which of the following statements about standing sound waves in a tube with both ends open is correct?

Accepted Answer

Displacement antinodes occur at both ends of the tube.

Question 6

A standing wave in a pipe has a frequency of $$440 Hz. $$The next higher harmonic has a frequency of $$660 Hz. $$The speed of sound is $$340 m/s. If $$both ends are open, what is the length $$L of $$the pipe?

Accepted Answer

$$L = 0.386 m$

Question 7

What is the relationship between intensity $$I$$ and pressure amplitude $$\Delta P_{	ext{max}} in a $$sound wave?

Accepted Answer

$$I \propto \Delta P_{	ext{max}}^2$$

Question 8

If the threshold of hearing at $$1$$ kHz is $$I_0$$ = $$10^{-12} W/m$^2$$, what is the intensity $$I$$ corresponding to a sound level of $$50 dB$$?

Accepted Answer

$$I = 10$$^{-7}$$ W/m^2$

Question 9

A $$3-$$meter long chimney moans at its fundamental frequency. If the speed of sound is $$340 m/s$$, what is the frequency of the sound produced?

Accepted Answer

$$f = \frac{340}{4 	imes 3}$$

Question 10

In a sound wave, what is the phase relationship between displacement maxima and pressure maxima?

Accepted Answer

Displacement maxima coincide with zero excess pressure.

Question 11

For a tube with one end open and one end closed, which harmonics are allowed?

Accepted Answer

Only odd harmonics (n = 1, 3, 5, ...)

Question 12

A sound wave in air has a frequency of $$1000 Hz $$and a wavelength of $$0.34 m. $$What is the speed of sound in air?

Accepted Answer

$$v = 340 m/s$$

Question 13

Which of the following best describes the boundary conditions for displacement and pressure at the closed end of a tube?

Accepted Answer

Displacement node, pressure antinode

Question 14

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

Accepted Answer

It increases.

Question 15

A sound wave has a displacement amplitude $$A$$ and angular frequency $$\omega. $$What is the total energy transferred per unit time through unit area (intensity) if the density of the medium is $$\rho$$ and the speed of sound is $$v$$?

Accepted Answer

$$I = \frac{1}{2} \$$omega^2$$ A^2$ \rho v$$

Question 16

If the intensity of a sound wave is $$I = 1 W/m$^2$$, what is the sound level in decibels ($$\beta) $$relative to the threshold of hearing $$I_0$$ = $$10^{-12} W/m$^2$$?

Accepted Answer

$$\beta = 120 dB$$

Question 17

A tube with both ends open supports a standing wave. What is the wavelength $$\lambda of $$the nth normal mode if the length of the tube is $$L$$?

Accepted Answer

$$\lambda = \frac{2L}{n}$$

Question 18

In a tube with one end open and one end closed, what is the wavelength $$\lambda of $$the nth normal mode?

Accepted Answer

$$\lambda = \frac{4L}{2n+1}$$

Question 19

A sound wave in a tube causes a small element of the medium to oscillate. If the element has mass $$\Delta m = \rho S \Delta x$$ and undergoes simple harmonic motion with angular frequency $$\omega$$ and amplitude $$A$$, what is the energy of this oscillator?

Accepted Answer

$$\Delta E = \frac{1}{2} \Delta m \$$omega^2$$ A^2$

Sound Intensity and Standing Sound Waves: Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards