Q: A violin string of length $$0.32\ \mathrm{m} is $$tuned to $$440\ \mathrm{Hz} (A $$above middle C). What is the speed of the wave on the string?

$$v = f \lambda = 440 \times 0.64 = 282\ \mathrm{m/s}$$

Question 1

A copper wire of length 30 m and diameter 2.10 mm is stretched with a tension $$F_T. If $$the mass density of copper is $$8.96 	imes 10^3$ \ \mathrm{kg/m^3$}$$, what is the speed of a transverse wave on the wire?

Accepted Answer

$$v = \sqrt{\frac{F_T}{\mu}}$$, where $$\mu = \rho \cdot A$$ and $$A = \pi r^2$

Question 2

Which equation correctly describes the displacement $$D(x,t) of a $$sinusoidal wave traveling in the positive $$x-$$direction?

Accepted Answer

$$D(x,t) = A \sin(kx - \omega t)$$

Question 3

A string of length $$L is $$fixed at both ends. What is the wavelength of the $$nth $$harmonic?

Accepted Answer

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

Question 4

The frequency of the third harmonic ($$n=3) $$for a string fixed at both ends is:

Accepted Answer

$$f_3 = 3f_1$

Question 5

A violin string of length $$0.32\ \mathrm{m} is $$tuned to $$440\ \mathrm{Hz} (A $$above middle C). What is the speed of the wave on the string?

Accepted Answer

$$v = f \lambda = 440 	imes 0.64 = 282\ \mathrm{m/s}$$

Question 6

Which of the following best describes the relationship between frequency and length for a string fixed at both ends?

Accepted Answer

$$f \propto \frac{1}{L}$$

Question 7

A disk spins at $$7200\ \mathrm{rpm}. $$What is its angular velocity in $$\mathrm{rad/s}$$?

Accepted Answer

$$\omega = 754\ \mathrm{rad/s}$$

Question 8

The torque $$	au$$ produced by a force $$F$$ applied at a distance $$R$$ from the pivot at an angle $$	heta is$$:

Accepted Answer

$$	au = RF \sin 	heta$$

Question 9

Which of the following is the correct formula for the period $$T of a $$mass-spring system in simple harmonic motion?

Accepted Answer

$$T = 2\pi \sqrt{\frac{m}{k}}$$

Question 10

A standing wave is formed on a string. Which statement is true about the nodes and antinodes?

Accepted Answer

Nodes are points of zero displacement, antinodes are points of maximum displacement.

Question 11

The general equation for a wave with a phase shift $$\phi is$$:

Accepted Answer

$$D(x,t) = A \sin(kx - \omega t + \phi)$$

Question 12

The speed of sound in air at room temperature is approximately:

Accepted Answer

$$343\ \mathrm{m/s}$$

Question 13

Which of the following is the correct relationship for the angular frequency $$\omega of a $$simple harmonic oscillator?

Accepted Answer

$$\omega = 2\pi f$$

Question 14

A string has a mass per unit length $$\mu$$ and is under tension $$F_T. $$What is the correct formula for the wave speed?

Accepted Answer

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

Question 15

The absolute temperature scale is called:

Accepted Answer

Kelvin

Question 16

If the temperature is $$37^\circ \mathrm{C}$$, what is the temperature in Kelvin?

Accepted Answer

$$310.15\ \mathrm{K}$$

Question 17

Which of the following best describes constructive interference?

Accepted Answer

When two waves meet in phase and their amplitudes add.

Question 18

A mass-spring system oscillates with amplitude $$A$$ and angular frequency $$\omega. $$What is the maximum speed of the mass?

Accepted Answer

$$v_{max} = A\omega$$

Question 19

Which of the following is the correct formula for the frequency of the $$nth $$harmonic for a string fixed at both ends?

Accepted Answer

$$f_n = n f_1$

Wave Motion, Sound, and Rotational Dynamics: Study Notes

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