Question 1

Which of the following best describes the principle of superposition for waves?

Accepted Answer

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

Question 2

Two sinusoidal waves of equal amplitude and frequency travel in opposite directions along a string. What is the resulting wave called?

Accepted Answer

A standing wave

Question 3

At what points along a standing wave on a string is the intensity of the wave maximum?

Accepted Answer

At the antinodes

Question 4

A string of length $$L is $$fixed at both ends. What is the wavelength of the fundamental mode of vibration?

Accepted Answer

$$\$$lambda_1$$ = 2L$$

Question 5

A wave pulse travels from a thick string (high linear density) to a thin string (low linear density) with the same tension. What happens to the transmitted and reflected pulses?

Accepted Answer

The transmitted pulse is faster and the reflected pulse is upright.

Question 6

When a wave reflects from a boundary where the wave speed decreases (e.g., from a light to a heavy string), what happens to the reflected wave?

Accepted Answer

It is inverted and has the same amplitude.

Question 7

The Tacoma Narrows Bridge collapsed due to which physical phenomenon?

Accepted Answer

Resonance and the formation of a standing wave due to wind-induced vibrations.

Question 8

For a standing wave on a string, the amplitude function is given by $$A(x) = 2a \sin(kx). $$What is the maximum amplitude of the standing wave?

Accepted Answer

$$2a$$

Question 9

A flute can be modeled as an open-open tube of length $$L. $$What is the fundamental frequency of the sound produced, given the speed of sound $$v$$?

Accepted Answer

$$f_1 = v/2L$

Question 10

A clarinet can be modeled as an open-closed tube of length $$L. $$What is the fundamental frequency of the sound produced, given the speed of sound $$v$$?

Accepted Answer

$$f_1 = v/4L$

Question 11

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

Accepted Answer

Nodes are points of zero displacement.

Question 12

In a closed-closed pipe of length $$L$$, what is the wavelength of the $$m-th $$mode?

Accepted Answer

$$\lambda_m = 2L/m$$

Question 13

If two waves of equal amplitude and frequency travel in the same direction and are perfectly out of phase, what is the resulting amplitude?

Accepted Answer

$$0$$

Question 14

A string of length $$L is $$vibrating in its third harmonic. How many antinodes are present?

Accepted Answer

3

Question 15

Which of the following best describes the energy flow at the nodes of a standing wave?

Accepted Answer

There is no energy flow through the nodes.

Question 16

A wave pulse reflects from a fixed boundary. What happens to the reflected pulse?

Accepted Answer

It is inverted and has the same amplitude.

Question 17

Which of the following is true for the frequencies of the normal modes of a string fixed at both ends?

Accepted Answer

They are integer multiples of the fundamental frequency.

Question 18

In a standing sound wave in a tube open at both ends, what is the boundary condition at each end?

Accepted Answer

Displacement antinode and pressure node

Question 19

Which equation correctly gives the frequency of the $$n-th $$harmonic for an open-open pipe of length $$L$$ and sound speed $$v$$?

Accepted Answer

$$f_n = nv/2L$$

Question 20

Which of the following best describes constructive interference?

Accepted Answer

Two waves are in phase and their amplitudes add.

Chapter 17: Superposition and Interference of Waves

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