Question 1

Which of the following statements correctly describes a mechanical wave?

Accepted Answer

A mechanical wave is a disturbance in a medium that travels at a well-defined velocity, carrying energy and momentum but not mass.

Question 2

Which type of wave has the motion of the medium perpendicular to the direction of wave propagation?

Accepted Answer

Transverse wave

Question 3

A wave pulse is best described as:

Accepted Answer

A localized disturbance that travels through the medium at the medium's wave velocity.

Question 4

Which of the following is NOT an example of a mechanical wave?

Accepted Answer

Light wave

Question 5

For a periodic wave, which property describes the maximum displacement of a point on the wave?

Accepted Answer

Amplitude $$A$$

Question 6

The period $$T of a $$wave is related to its frequency $$f by $$which equation?

Accepted Answer

$$T = \frac{1}{f}$$

Question 7

A sinusoidal wave on a string is described by $$x(t) = A \cos(\omega t + \phi). $$What is the velocity of the particle at $$t=0$$?

Accepted Answer

$$v(0) = -A \omega \sin(\phi)$$

Question 8

The speed $$v of a $$wave on a string depends on which of the following?

Accepted Answer

The tension and mass per unit length of the string

Question 9

Given a wave with wavelength $$\lambda = 20\,\mathrm{m}$$ and speed $$v = 5\,\mathrm{m/s}$$, what is the period $$T of $$the wave?

Accepted Answer

$$T = 4\,\mathrm{s}$$

Question 10

For a string of length $$L$$ with both ends fixed, what is the wavelength $$\lambda of $$the fundamental mode (first harmonic)?

Accepted Answer

$$\lambda = 2L$$

Question 11

Which equation correctly gives the wave function for a sinusoidal wave moving in the $$+x$$ direction?

Accepted Answer

$$y(x,t) = A \cos(\omega t - kx)$$

Question 12

If the tension in a string is increased, what happens to the speed of a wave traveling on the string?

Accepted Answer

The speed increases.

Question 13

The principle of superposition states that:

Accepted Answer

The wave displacements at a point simply add when two waves meet.

Question 14

For a standing wave on a string, what are the positions called where the displacement is always zero?

Accepted Answer

Nodes

Question 15

A musical instrument has six strings of the same material and tension but different thicknesses. On which string does the wave travel fastest?

Accepted Answer

On the thinnest string

Question 16

Which of the following is true about the speed of a mechanical wave?

Accepted Answer

It is a constant that depends only on the properties of the medium.

Question 17

The wave function $$y(x,t) = A \cos(\omega t - kx)$$ describes:

Accepted Answer

A wave moving in the $$+x$$ direction

Question 18

For a standing wave on a string of length $$L$$ with both ends fixed, what is the allowed wavelength for the $$nth $$harmonic?

Accepted Answer

$$\lambda_n = \frac{2L}{n}$$

Question 19

Which property of a wave is defined as the distance between identical points on consecutive cycles?

Accepted Answer

Wavelength

Question 20

A sinusoidal wave is described by $$y(x,t) = A \cos(\omega t - kx). $$What is the value of $$k in $$terms of wavelength $$\lambda$$?

Accepted Answer

$$k = \frac{2\pi}{\lambda}$$

Mechanical Waves: Properties, Types, and Wave Functions

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