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

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

Question 1

Which principle explains the phenomenon shown in the first image, where three different waves combine to form a complex wave?

Accepted Answer

The Principle of Superposition

Question 2

In the context of wave motion, what does Fourier’s theorem state?

Accepted Answer

Any complex wave can be decomposed into a series of simple sinusoidal waves.

Question 3

Refer to the third image. What happens to a wave pulse when it reaches a fixed end?

Accepted Answer

It is reflected and inverted.

Question 4

A wave pulse travels from a light string to a heavy string, as shown in the fourth image. What happens to the reflected and transmitted pulses?

Accepted Answer

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

Question 5

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

Accepted Answer

By drawing a tangent line connecting the secondary wavelets from each point on the old wavefront.

Question 6

Which equation correctly expresses the law of reflection for waves?

Accepted Answer

$$	heta_i = 	heta_r$$

Question 7

If two waves of equal amplitude and frequency travel in opposite directions and interfere, what type of wave is formed?

Accepted Answer

A standing wave

Question 8

Given the standing wave equation $$y(x, t) = 2A \sin(kx) \cos(\omega t)$$, what is the distance between two adjacent nodes?

Accepted Answer

$$\lambda / 2$$

Question 9

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 angle of refraction $$	heta_r$$? (Use $$\sin 	heta_r = \frac{v_2$}{v_1$} \sin 	heta_i)$$

Accepted Answer

$$32^\circ$$

Question 10

Which of the following best describes diffraction?

Accepted Answer

The bending of waves around obstacles or through openings.

Question 11

What is the mathematical condition for constructive interference between two waves?

Accepted Answer

The waves are in phase ($$\Delta \phi = 0 or $$integer multiples of $$2\pi)$$

Question 12

A string of length $$L is $$fixed at both ends. What is the fundamental wavelength $$\$$lambda_1$$ of the standing wave?

Accepted Answer

$$2L$$

Question 13

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

Accepted Answer

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

Question 14

If a wave is described by $$y(x, t) = A \sin(kx - \omega t)$$, what is the phase velocity $$v of $$the wave?

Accepted Answer

$$v = \omega / k$$

Question 15

In a standing wave, what are the points called where the displacement is always zero?

Accepted Answer

Nodes

Question 16

A wave pulse on a string is partially reflected and partially transmitted at a boundary. If the transmitted pulse has a lower amplitude than the incident pulse, what does this indicate?

Accepted Answer

Some energy is reflected back at the boundary.

Question 17

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

Accepted Answer

Waves always cancel each other out completely.

Question 18

What is the amplitude of the standing wave $$y(x, t) = 6.4 \sin(0.40x) \cos(35t)$$?

Accepted Answer

$$3.2$$

Question 19

Which of the following best describes a wavefront?

Accepted Answer

A continuous line or surface representing points of equal phase, such as crests or troughs.

Question 20

A standing wave on a string has nodes at $$x = 0$$ and $$x = L. $$What is the condition for the allowed wavelengths?

Accepted Answer

$$\lambda_n = \frac{2L}{n}$$, where $$n = 1, 2, 3, ...$$

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

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