Q: A sound wave travels from warm air ($$v_1 = 346$$\ \mathrm{m/s}$$) into cold air (v_2$ = 321\ \mathrm{m/s}) at an $$incident angle of $$35^\circ. $$What is the equation for the angle of refraction $$\theta_r$$?

$$\sin \theta_r = \frac{v_1$}{v_2$} \sin \theta_i$$

Q: Which equation represents Snell’s law for refraction of waves?

$$\frac{\sin \theta_i}{\sin \theta_r} = \frac{v_1$}{v_2$}$$

Question 1

According to the principle of superposition, what is the resulting displacement at a point where two waves overlap?

Accepted Answer

The algebraic sum of the individual displacements.

Question 2

Which mathematical tool allows us to express a complex wave as a sum of simple sinusoidal waves?

Accepted Answer

Fourier's theorem

Question 3

A wave pulse traveling on a string reaches a fixed end. What happens to the pulse upon reflection?

Accepted Answer

It reflects and is inverted.

Question 4

When a wave pulse travels from a light string to a heavy string, what happens at the boundary?

Accepted Answer

The pulse is reflected and inverted, and a smaller upright pulse is transmitted.

Question 5

Which of the following best describes a wave front?

Accepted Answer

A continuous line corresponding to a crest or trough.

Question 6

According to Huygen’s principle, how is a new wave front constructed?

Accepted Answer

By connecting the tangent points of secondary wavelets from each point on the old wave front.

Question 7

Fermat’s principle of least time states that:

Accepted Answer

The path taken by a ray of light between two points is the one that takes the least time.

Question 8

Which equation represents the law of reflection?

Accepted Answer

$$	heta_i = 	heta_r$$

Question 9

Two waves of equal amplitude and frequency travel in opposite directions and interfere. What is the result?

Accepted Answer

A standing wave with nodes and antinodes.

Question 10

For a string of length $$L$$ fixed at both ends, what is the wavelength of the fundamental mode?

Accepted Answer

$$\lambda = 2L$$

Question 11

A sound wave travels from warm air ($$v_1 = 346$$\ \mathrm{m/s}$$) into cold air (v_2$ = 321\ \mathrm{m/s}) at an $$incident angle of $$35^\circ. $$What is the equation for the angle of refraction $$	heta_r$$?

Accepted Answer

$$\sin 	heta_r = \frac{v_1$}{v_2$} \sin 	heta_i$$

Question 12

Which of the following is true about nodes in a standing wave?

Accepted Answer

They are points where the displacement is always zero.

Question 13

What is the speed $$v of a $$wave given by $$y(x, t) = A \sin(kx - \omega t)$$?

Accepted Answer

$$v = \omega / k$$

Question 14

Which phenomenon explains why sound can be heard around a corner?

Accepted Answer

Diffraction

Question 15

If two waves are out of phase by $$\pi$$ radians, what type of interference occurs?

Accepted Answer

Destructive interference

Question 16

A standing wave on a string is described by $$y(x, t) = 2A \sin(kx) \cos(\omega t). $$What is the maximum amplitude at an antinode?

Accepted Answer

$$2A$$

Question 17

Which equation represents Snell’s law for refraction of waves?

Accepted Answer

$$\frac{\sin 	heta_i}{\sin 	heta_r} = \frac{v_1$}{v_2$}$$

Question 18

A sawtooth wave can be synthesized by summing which type of functions?

Accepted Answer

A series of sine functions with all harmonics

Question 19

What happens to the direction of a wave when it passes into a medium where its speed increases?

Accepted Answer

It bends away from the normal.

Question 20

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

Accepted Answer

A point where the displacement reaches its maximum value.

Wave Motion: Superposition, Reflection, Transmission, Refraction, and Standing Waves

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