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 sound waves of equal amplitude and frequency travel in opposite directions and interfere. What is the resulting phenomenon called?

Accepted Answer

Standing wave

Question 3

At a node in a standing wave on a string, what is the displacement of the medium?

Accepted Answer

Zero

Question 4

A string of length $$L is $$fixed at both ends. What is the wavelength $$\lambda_m of $$the $$mth $$standing wave mode?

Accepted Answer

$$\$$\lambda_m = \frac{2L}{m}\$$ for m = 1$$, 2, 3, ...$

Question 5

Which of the following statements about constructive interference is correct?

Accepted Answer

It occurs when two waves of the same sign overlap, resulting in a displacement larger than either wave alone.

Question 6

A wave pulse traveling along a string is reflected from a fixed boundary. What happens to the pulse?

Accepted Answer

It is reflected with the same amplitude and is inverted.

Question 7

If a string supports a standing wave with three antinodes, what is the mode number $$m$$?

Accepted Answer

$$m = 3$$

Question 8

The frequency of the $$mth $$standing wave mode on a string of length $$L$$ and wave speed $$v is $$given by:

Accepted Answer

$$\f_m$$ = \frac{mv}{2L}\$$ for m = 1$$, 2, 3, ...$

Question 9

Which of the following best describes an antinode in a standing wave?

Accepted Answer

A point where the displacement is maximum

Question 10

A string of length $$L = 1.2\,\mathrm{m} is $$fixed at both ends and supports a standing wave at its second harmonic. If the wave speed is $$v = 60\,\mathrm{m/s}$$, what is the frequency of this mode?

Accepted Answer

$$\f_2$ = 50\,\mathrm{Hz}\$

Question 11

Which of the following is true about the harmonics of a string fixed at both ends?

Accepted Answer

The frequencies of the harmonics are integer multiples of the fundamental frequency.

Question 12

A wave pulse travels from a light string to a heavier string. What happens at the boundary?

Accepted Answer

The reflected pulse is inverted and the transmitted pulse has smaller amplitude.

Question 13

In a standing wave, the distance between two adjacent nodes is:

Accepted Answer

$$\$$\frac{\lambda}{2}\$

Question 14

Which of the following real-world examples best illustrates the concept of standing waves?

Accepted Answer

The vibration of a guitar string fixed at both ends

Question 15

If two waves with equal amplitude and opposite phase meet at a point, what type of interference occurs?

Accepted Answer

Destructive interference

Question 16

A string of length $$L is $$vibrating in its third harmonic. How many nodes (including the ends) are present?

Accepted Answer

4

Question 17

Which of the following is NOT a requirement for a standing wave to form on a string fixed at both ends?

Accepted Answer

The string must be plucked exactly in the middle.

Question 18

A standing wave on a string has a frequency $$f_1$$ for its fundamental mode. What is the frequency of the third harmonic?

Accepted Answer

$$3f_1$$

Question 19

Which of the following best explains why sound waves from two loudspeakers can pass through each other without being destroyed?

Accepted Answer

Sound waves obey the principle of superposition.

Superposition and Standing Waves: Chapter 16 Study Notes

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