Question 1

Which of the following best describes a standing wave in a tube that is closed at one end and open at the other?

Accepted Answer

Nodes are always at the closed end and antinodes at the open end.

Question 2

According to Fourier’s theorem, any complex sound can be represented as:

Accepted Answer

A sum of sine waves with different amplitudes, frequencies, and phases.

Question 3

A tube open at both ends resonates at its fundamental frequency. If the length of the tube is $$L$$ and the speed of sound is $$v$$, what is the wavelength $$\lambda of $$the fundamental mode?

Accepted Answer

$$\lambda = 2L$$

Question 4

Which of the following statements about nodes and antinodes in standing waves is correct?

Accepted Answer

Nodes are points of zero vibration, and antinodes are points of maximum vibration.

Question 5

A complex periodic sound is composed of a 100 Hz fundamental frequency and its first three harmonics. What are the frequencies of these harmonics?

Accepted Answer

100 Hz, 200 Hz, 300 Hz, 400 Hz

Question 6

If the duration of an acoustic transient (click) is very short, what can be said about its frequency spectrum?

Accepted Answer

The frequency spectrum is broad.

Question 7

Which equation correctly describes an amplitude modulated (AM) signal where $$A is $$amplitude, $$F_c is $$carrier frequency, $$F_m is $$modulation frequency, and $$m is $$modulation index?

Accepted Answer

$$D(t) = A \cdot [1 + m \cdot \sin(2\pi F_m t)] \cdot \sin(2\pi F_c t)$$

Question 8

A square wave can be synthesized by adding which of the following?

Accepted Answer

Only the odd harmonics of the fundamental frequency.

Question 9

If two sine waves of frequencies $$f_1$$ and $$f_2 ($$with $$f_2$$ \u003e $$f_1) $$are added together and $$f_1$$ and $$f_2$$ are close in value, what is the perceived frequency of the beating stimulus?

Accepted Answer

$$(f_1$ + f_2$)/2$$

Question 10

Which of the following is true about the effect of changing the relative phase of harmonics in a complex sound?

Accepted Answer

It changes the time domain display but not the magnitude spectrum.

Question 11

A tube closed at one end and open at the other resonates at its fundamental frequency. If the tube length is $$L$$, what is the wavelength $$\lambda of $$the fundamental mode?

Accepted Answer

$$\lambda = 4L$$

Question 12

Which of the following best describes the amplitude spectrum of a click (acoustic transient) with a very short duration?

Accepted Answer

It is a continuous spectrum with amplitude going to zero at frequencies related to integer multiples of the signal duration.

Question 13

Which of the following is NOT a correct statement about standing waves?

Accepted Answer

Nodes are points of maximum vibration.

Question 14

In the context of sound waves, what does the frequency domain display show?

Accepted Answer

The amplitude and phase of each frequency component.

Question 15

A bat uses frequency modulated (FM) calls for echolocation. Which of the following best describes a frequency modulated signal?

Accepted Answer

A signal in which the frequency varies as a function of time.

Question 16

If the amplitude of higher harmonics in a complex sound decreases, what is the effect on the time domain and frequency domain displays?

Accepted Answer

Both the time domain and frequency domain displays are altered.

Question 17

Which of the following is a correct statement about the harmonics of a complex periodic sound?

Accepted Answer

Harmonics are integer multiples of the fundamental frequency.

Question 18

Which of the following best describes the effect of amplitude modulation (AM) when two sine waves of close frequencies are added together?

Accepted Answer

The resulting signal exhibits beats, with loudness changes at a rate equal to the difference of the two frequencies.

Waves, Standing Waves, and Fourier Analysis in Physics with Calculus

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