Q: A string of length $$L = 1.2\ \mathrm{m} is $$fixed at both ends and has a mass per unit length $$\mu = 0.01\ \mathrm{kg/m}. If $$the tension in the string is $$T = 48\ \mathrm{N}$$, what is the fundamental frequency $$f_1$$?

$$f_1$$ = \frac{1}{2L} \sqrt{\frac{T}{\mu}} = \frac{1}{2 \times 1.2} \sqrt{\frac{48}{0.01}} \approx 10\ \mathrm{Hz}$$

Question 1

Which of the following statements best describes the difference between mechanical and electromagnetic waves?

Accepted Answer

Mechanical waves require a medium for propagation, while electromagnetic waves do not.

Question 2

A string is fixed at both ends and vibrates in its second harmonic. If the length of the string is $$L$$, what is the wavelength $$\$$lambda_2$$ of the second harmonic?

Accepted Answer

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

Question 3

Which equation correctly relates the speed $$v of a $$wave on a string to the tension $$T$$ and the mass per unit length $$\mu$$?

Accepted Answer

$$v = \sqrt{\frac{T}{\mu}}$$

Question 4

A sinusoidal wave is described by $$y(x,t) = A \cos(kx - \omega t). $$What does the parameter $$A$$ represent?

Accepted Answer

The amplitude of the wave

Question 5

A sound wave travels through air and causes the air molecules to oscillate back and forth in the direction of propagation. What type of wave is this?

Accepted Answer

Longitudinal wave

Question 6

If the frequency of a wave is doubled while its speed remains constant, what happens to its wavelength?

Accepted Answer

The wavelength is halved.

Question 7

A string of length $$L is $$fixed at both ends. Which of the following expressions gives the frequency of the $$nth $$harmonic?

Accepted Answer

$$f_n = \frac{n}{2L} \sqrt{\frac{T}{\mu}}$$

Question 8

Which of the following best describes a node in a standing wave?

Accepted Answer

A point where the amplitude is always zero.

Question 9

A wave on a string is reflected from a fixed end. What happens to the reflected pulse?

Accepted Answer

It is inverted and travels in the opposite direction.

Question 10

A string of length $$L = 1.2\ \mathrm{m} is $$fixed at both ends and has a mass per unit length $$\mu = 0.01\ \mathrm{kg/m}. If $$the tension in the string is $$T = 48\ \mathrm{N}$$, what is the fundamental frequency $$f_1$$?

Accepted Answer

$$f_1$$ = \frac{1}{2L} \sqrt{\frac{T}{\mu}} = \frac{1}{2 	imes 1.2} \sqrt{\frac{48}{0.01}} \approx 10\ \mathrm{Hz}$$

Question 11

Which of the following is true about the energy transfer in wave motion?

Accepted Answer

Energy is transferred, but matter is not transferred over a distance.

Question 12

A standing wave is formed on a string fixed at both ends. If the distance between two adjacent nodes is $$0.5\ \mathrm{m}$$, what is the wavelength of the wave?

Accepted Answer

$$\lambda = 1.0\ \mathrm{m}$$

Question 13

Which of the following best describes the relationship between period $$T$$ and frequency $$f of a $$wave?

Accepted Answer

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

Question 14

A wave is described by $$y(x,t) = 0.10 \cos(4\pi x - 20\pi t)$$, where $$x$$ and $$y$$ are in meters and $$t is in $$seconds. What is the wavelength $$\lambda$$?

Accepted Answer

$$\lambda = \frac{2\pi}{k} = \frac{2\pi}{4\pi} = 0.5\ \mathrm{m}$$

Question 15

Which of the following is a correct statement about the harmonic series for a string fixed at both ends?

Accepted Answer

The frequencies of the harmonics are integer multiples of the fundamental frequency.

Question 16

A wave pulse is traveling to the right along a string. Which equation describes the wave function $$y(x,t)$$ for this pulse?

Accepted Answer

$$y(x,t) = f(x - vt)$$

Question 17

In a standing wave, what is the distance between a node and the nearest antinode?

Accepted Answer

$$\lambda/4$$

Question 18

A guitar string is tightened, increasing the tension. What happens to the speed of waves on the string?

Accepted Answer

The speed increases because $$v = \sqrt{\frac{T}{\mu}}.$$

Question 19

Which of the following is NOT a requirement for the propagation of a mechanical wave?

Accepted Answer

A vacuum

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