Q: Which equation would you use to calculate the intensity of a sound given its sound level $$\beta in $$decibels?

$$I = (I_0$) 10$$^{\beta/(10\ \text{dB}$$)}$$

Question 1

Which type of wave is illustrated by the concentric ripples seen in the first image, and what is the primary characteristic of its wave fronts?

Accepted Answer

Circular wave; wave fronts are concentric circles that spread outward from the source.

Question 2

A spherical wave radiates from a point source. If the power emitted by the source is $$P$$, what is the intensity $$I at a $$distance $$r$$ from the source?

Accepted Answer

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

Question 3

If a plane wave, a circular wave, and a spherical wave all start with the same intensity and travel the same distance, which wave will have the highest intensity after traveling?

Accepted Answer

The plane wave

Question 4

A siren emits sound uniformly in all directions. At 15.0 m from the siren, the intensity is $$0.250\ 	ext{W/m}^2. At $$what distance will the intensity be $$0.010\ 	ext{W/m}^2$$?

Accepted Answer

75.0 m

Question 5

The threshold of hearing for the average human ear is $$I_0 = 1.0$$ 	imes $$10^{-12}$$\ 	ext{W/m}^2$$. What is the sound level in decibels for a sound with intensity I = 1.0$$ 	imes $$10^{-6}$$\ 	ext{W/m}^2$$?

Accepted Answer

$$\beta = 60\ 	ext{dB}$$

Question 6

If the intensity of a sound decreases by a factor of 100, how does the sound level in decibels change?

Accepted Answer

It decreases by 20 dB

Question 7

What is the intensity of a sound with a sound level of $$115\ 	ext{dB}$$?

Accepted Answer

$$I = 0.316\ 	ext{W/m}^2$$

Question 8

According to the principle of superposition, what happens when two waves pass through the same region of space at the same time?

Accepted Answer

The displacement at each point is the sum of the displacements due to each wave.

Question 9

Which scenario best describes constructive interference?

Accepted Answer

Two waves overlap to produce a resultant displacement greater than either individual wave.

Question 10

A standing wave forms on a string fixed at one end. What are the points called where the string remains still at all times?

Accepted Answer

Nodes

Question 11

A standing wave is set up on a string of length $$3.0\ 	ext{m}$$, and there are three antinodes. What is the wavelength of the standing wave?

Accepted Answer

$$\lambda = 1.0\ 	ext{m}$$

Question 12

Which equation describes the displacement $$y(x, t) of a $$sinusoidal travelling wave of amplitude $$A$$, wavelength $$\lambda$$, and period $$T$$?

Accepted Answer

$$y(x, t) = A \cos \left( 2\pi \left( \frac{x}{\lambda} \pm \frac{t}{T} \right) \right)$$

Question 13

In the context of sound waves, what is the relationship between perceived loudness and intensity for frequencies near the middle of the audible range?

Accepted Answer

Perceived loudness doubles when intensity increases by a factor of 10.

Question 14

If two wave pulses on a string approach each other and overlap, what happens to the shape of the string at the moment they overlap?

Accepted Answer

The string's displacement is the sum of the individual pulses.

Question 15

Which of the following best describes a node in a standing wave?

Accepted Answer

A point of destructive interference where the string remains still.

Question 16

A sound has an intensity of $$1.0 	imes 10$$^{-3}$$\ 	ext{W/m}^2. $$What is its sound level in decibels?

Accepted Answer

$$\beta = 90\ 	ext{dB}$$

Question 17

Which equation would you use to calculate the intensity of a sound given its sound level $$\beta in $$decibels?

Accepted Answer

$$I = (I_0$) 10$$^{\beta/(10\ 	ext{dB}$$)}$$

Question 18

Which of the following is NOT a consequence of the principle of superposition?

Accepted Answer

Waves can reflect off each other and change direction.

Waves and Sound II: Energy, Intensity, Decibels, and Standing Waves

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