Question 1

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

Accepted Answer

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

Question 2

Two pulses traveling in opposite directions on a string overlap. If both pulses have positive displacement, what type of interference occurs at the point of overlap?

Accepted Answer

Constructive interference

Question 3

A standing wave on a string fixed at both ends has nodes at $$x = 0$$ and $$x = L. $$What is the wavelength of the fundamental mode?

Accepted Answer

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

Question 4

The intensity of a wave is proportional to which of the following?

Accepted Answer

$$I \propto A^2$

Question 5

A string of length $$L is $$fixed at both ends. Which equation gives the allowed frequencies for standing waves on the string?

Accepted Answer

$$f_m = \dfrac{m v}{2L}$$

Question 6

Two identical loudspeakers emit sound waves of wavelength $$\lambda$$ and are separated by a distance $$d = \lambda/2. At a $$point directly in front of one speaker, what type of interference occurs?

Accepted Answer

Destructive interference

Question 7

A thin film of oil ($$n = 1.42) of $$thickness $$t$$ coats a glass surface. For constructive interference of reflected light (with a 180° phase shift at the top surface), which condition must be satisfied?

Accepted Answer

$$2t = (m + 1/2) \lambda_n$$

Question 8

A wave traveling on a string encounters a boundary where the wave speed decreases. What happens to the reflected wave?

Accepted Answer

It is reflected with a phase change of $$\pi ($$inverted).

Question 9

In a tube open at one end and closed at the other, which harmonics are present in the standing wave patterns?

Accepted Answer

Only odd harmonics (m = 1, 3, 5, ...)

Question 10

Two waves of equal amplitude $$a$$ and frequency travel in the same direction but are out of phase by $$\Delta \phi = \pi. $$What is the amplitude of the resultant wave?

Accepted Answer

0

Question 11

A soap bubble displays a variety of colors when illuminated by white light. This phenomenon is primarily due to:

Accepted Answer

Interference of light reflected from the two surfaces of the film

Question 12

A standing wave is described by $$y(x, t) = 0.10 \sin(\pi x) \cos(20 \pi t)$$, where $$x$$ and $$y$$ are in meters and $$t in $$seconds. What is the wavelength of the standing wave?

Accepted Answer

$$1.0 m$$

Question 13

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

Accepted Answer

3

Question 14

Two in-phase sound sources emit waves of equal wavelength and intensity. At a point where the path-length difference is $$\Delta r = \lambda$$, what type of interference occurs?

Accepted Answer

Constructive interference

Question 15

A wave on a string is described by $$y(x, t) = a \sin(kx - \omega t). $$What is the speed of the wave?

Accepted Answer

$$v = \omega / k$$

Question 16

A 25 cm long wire with a linear density of 20 g/m vibrates at its fundamental frequency above an 85 cm long open-closed tube of air, exciting the tube's second vibrational mode. If the speed of sound in air is $$340 m/s$$, which equation would you use to find the tension in the wire?

Accepted Answer

$$f_{wire} = \dfrac{1}{2L_{wire}} \sqrt{\dfrac{T}{\mu}}$$

Question 17

In a thin film interference problem, if the film is between two different media (one with $$n_1  n$$_{film}$$), what must you check to determine the interference condition?

Accepted Answer

Both the path length difference and phase changes at both surfaces

Chapter 17: Superposition and Interference of Waves

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