Question 1

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

Accepted Answer

When two or more waves are present at a point, the displacement of the medium is the sum of the displacements due to each individual wave.

Question 2

A wave pulse on a string reflects from a hard boundary. How is the reflected pulse related to the incident pulse?

Accepted Answer

Shape inverted, amplitude unchanged

Question 3

What are the points on a standing wave that never move called?

Accepted Answer

Nodes

Question 4

Two sound waves of nearly equal frequencies are played simultaneously. What is the name of the acoustic phenomenon you hear?

Accepted Answer

Beats

Question 5

The frequency of the third harmonic of a string is:

Accepted Answer

Three times the frequency of the fundamental.

Question 6

For a string of length $$L$$ fixed at both ends, what is the wavelength of the $$m-th $$normal mode?

Accepted Answer

$$\lambda_m = \dfrac{2L}{m}$$

Question 7

A standing wave on a string vibrates as shown. Suppose the string tension is reduced to $$1/4$$ its original value while the frequency and length are kept unchanged. What happens to the mode number $$m$$?

Accepted Answer

It is doubled.

Question 8

Which of the following best describes constructive interference?

Accepted Answer

Waves add to produce a wave with a larger amplitude.

Question 9

In a tube open at both ends, what is the fundamental frequency $$f_1 if $$the speed of sound is $$v$$ and the tube length is $$L$$?

Accepted Answer

$$f_1$$ = \dfrac{v}{2L}$$

Question 10

A thin film of oil (index $$n) of $$thickness $$d is on $$glass. For light of wavelength $$\lambda in $$air, what is the condition for constructive interference in the reflected light?

Accepted Answer

$$2nd = (m+\dfrac{1}{2})\lambda$$

Question 11

Two loudspeakers emit sound waves of the same amplitude and frequency. If one speaker is moved forward by half a wavelength, what type of interference occurs at a fixed point equidistant from both speakers?

Accepted Answer

Destructive interference

Question 12

The beat frequency heard when two sound sources of frequencies $$f_1$$ and $$f_2$$ are played together is:

Accepted Answer

$$|f_1$ - f_2$|$$

Question 13

A standing wave is created on a string of length $$L$$ fixed at both ends. How many nodes (including the ends) are present in the $$m-th $$mode?

Accepted Answer

$$m+1$$

Question 14

Which of the following is a real-world application of the principle of superposition?

Accepted Answer

The formation of beats in musical tuning

Question 15

In a closed-closed tube of length $$L$$, what is the wavelength of the second harmonic?

Accepted Answer

$$\$$lambda_2$$ = L$$

Question 16

If the speed of sound in air decreases due to a drop in temperature, what happens to the fundamental frequency of an open-open tube of fixed length?

Accepted Answer

It decreases.

Question 17

Which of the following best describes the difference between nodes and antinodes in a standing wave?

Accepted Answer

Nodes are points of zero displacement; antinodes are points of maximum displacement.

Question 18

A string of length $$L is $$vibrating in its third harmonic. What is the frequency of this mode if the wave speed is $$v$$?

Accepted Answer

$$f_3$$ = \dfrac{3v}{2L}$$

Question 19

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

Accepted Answer

Reflection of a single wave at a boundary

Chapter 17: Superposition and Interference of Waves

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