Q: A mass attached to a spring oscillates back and forth. Which equation best describes its displacement as a function of time in simple harmonic motion?

$$D(t) = A \cdot \sin(2\pi f t + \theta)$$

Q: If a pure sinusoidal sound wave has a peak amplitude ($$A_{\text{peak}}) of 10$$ µPa, what is its RMS amplitude ($$A_{\text{RMS}}$$)?

$$A_{\text{RMS}} = 7.07 \text{ µPa}$$

Q: A waveform has a peak amplitude of 30 µPa. What is its peak-to-peak amplitude?

$$A_{\text{P2P}} = 60 \text{ µPa}$$

Q: A waveform has an RMS amplitude of 14 µPa. What is its peak amplitude?

$$A_{\text{peak}} = 19.8 \text{ µPa}$$

Question 1

Which of the following best describes the relationship between sine and cosine functions as defined on the unit circle?

Accepted Answer

Sine tracks the y-coordinate and cosine tracks the x-coordinate, and they are always 90° out of phase.

Question 2

A mass attached to a spring oscillates back and forth. Which equation best describes its displacement as a function of time in simple harmonic motion?

Accepted Answer

$$D(t) = A \cdot \sin(2\pi f t + 	heta)$$

Question 3

If a pure sinusoidal sound wave has a peak amplitude ($$A_{	ext{peak}}) of 10$$ µPa, what is its RMS amplitude ($$A_{	ext{RMS}}$$)?

Accepted Answer

$$A_{	ext{RMS}} = 7.07 	ext{ µPa}$$

Question 4

A sound wave completes one cycle every 40 ms. What is its frequency in Hz?

Accepted Answer

$$f = 25 	ext{ Hz}$$

Question 5

Which physical parameter of a sound wave corresponds to the psychological perception of pitch?

Accepted Answer

Frequency

Question 6

If the speed of sound in water is $$c = 1500 	ext{ m/s}$$ and a tone has a frequency of $$f = 750 	ext{ Hz}$$, what is its wavelength ($$\lambda$$)?

Accepted Answer

$$\lambda = 2 	ext{ m}$$

Question 7

Which of the following statements about sound transmission is correct?

Accepted Answer

Sound requires a medium because particle displacement, velocity, acceleration, and pressure all depend on the presence of particles.

Question 8

What is the phase relationship between particle displacement and velocity in simple harmonic motion?

Accepted Answer

They are 90° out of phase.

Question 9

A waveform has a peak amplitude of 30 µPa. What is its peak-to-peak amplitude?

Accepted Answer

$$A_{	ext{P2P}} = 60 	ext{ µPa}$$

Question 10

Which equation correctly relates frequency ($$f) $$and period ($$T) of a $$sound wave?

Accepted Answer

$$T = 1 / f$$

Question 11

A guitar string vibrates at 440 Hz. If the speed of sound in air is 340 m/s, what is the wavelength of the sound produced?

Accepted Answer

$$\lambda = 0.77 	ext{ m}$$

Question 12

Which of the following best explains why the arithmetic average of a sinusoidal waveform is zero?

Accepted Answer

The positive and negative values cancel each other out over a cycle.

Question 13

In the context of sound waves, what does the variable $$	heta$$ represent in the equation $$D(t) = A \cdot \sin(2\pi f t + 	heta)$$?

Accepted Answer

Starting phase

Question 14

Which of the following is NOT an example of simple harmonic motion?

Accepted Answer

A car moving at constant speed in a straight line

Question 15

If two sine waves of the same frequency have a phase difference of $$90^\circ$$, what is the relationship between their waveforms?

Accepted Answer

One leads or lags the other by a quarter cycle.

Question 16

Which formula gives the wavelength ($$\lambda) of a $$sound wave in terms of the speed of sound ($$c) $$and frequency ($$f$$)?

Accepted Answer

$$\lambda = c / f$$

Question 17

During sound transmission, which pair of quantities is 180° out of phase?

Accepted Answer

Displacement and acceleration

Question 18

A waveform has an RMS amplitude of 14 µPa. What is its peak amplitude?

Accepted Answer

$$A_{	ext{peak}} = 19.8 	ext{ µPa}$$

Question 19

Which of the following best describes the relationship between air particle velocity and sound pressure during sound transmission?

Accepted Answer

They are in phase (0° apart).

Question 20

A signal completes one cycle every 0.01 seconds. What is its frequency?

Accepted Answer

$$f = 100 	ext{ Hz}$$

Sine and Cosine Functions, Simple Harmonic Motion, and Sound Wave Parameters

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