Question 1

A mass $$m is $$attached to a spring with spring constant $$k$$ and oscillates with no friction. What is the total mechanical energy $$E of $$the system if the amplitude of oscillation is $$A$$?

Accepted Answer

$$E = \frac{1}{2}kA^2$

Question 2

Which of the following best describes the restoring force acting on a mass-spring system in simple harmonic motion (SHM)?

Accepted Answer

It is proportional to the displacement and acts in the opposite direction.

Question 3

A physical pendulum of mass $$m$$ and length $$l$$ has a moment of inertia $$I$$ about the pivot. What is the angular frequency $$\omega of $$small oscillations?

Accepted Answer

$$\omega = \sqrt{\frac{mgl}{I}}$$

Question 4

For a lightly damped oscillator, the energy decays exponentially with time. If the initial energy is $$E_0$$, what is the energy $$E at $$time $$t$$?

Accepted Answer

$$E = E_0$ e$$^{-t/	au}$$

Question 5

A mass on a spring oscillates according to $$x(t) = A \cos(\omega t + \$$phi_0$$). $$What is the velocity $$v(t) at $$time $$t$$?

Accepted Answer

$$v(t) = -\omega A \sin(\omega t + \$$phi_0$$)$$

Question 6

Which of the following statements about mechanical and electromagnetic waves is correct?

Accepted Answer

Mechanical waves require a medium, while electromagnetic waves can travel through a vacuum.

Question 7

A sinusoidal wave is described by $$D(x, t) = A \sin(2\pi(x/\lambda - t/T)). $$What is the speed $$v of $$the wave?

Accepted Answer

$$v = \frac{\lambda}{T}$$

Question 8

The speed of sound in air at $$20^\circC is $$approximately:

Accepted Answer

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

Question 9

A stationary observer hears a sound from a moving source. If the source moves towards the observer with speed $$v_s$$, what is the observed frequency $$f_o$$?

Accepted Answer

$$f_o = f_s \left( \frac{v}{v - v_s} \right)$$

Question 10

A string fixed at both ends has length $$L. $$What is the wavelength $$\lambda_m of $$the $$mth $$harmonic?

Accepted Answer

$$\lambda_m = \frac{2L}{m}$$

Question 11

For a sound wave in an open-closed tube of length $$L$$, which of the following is true for the allowed wavelengths?

Accepted Answer

$$\lambda_m = \frac{4L}{m}$$, where $$m = 1, 3, 5, \ldots$$

Question 12

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

Accepted Answer

A standing wave is formed.

Question 13

A wave on a string is described by $$y(x, t) = A \sin(kx - \omega t). $$What is the direction of propagation of the wave?

Accepted Answer

In the $$+x$$ direction

Question 14

Which of the following best explains why the energy of a lightly damped oscillator decays exponentially?

Accepted Answer

Because the damping force removes a constant fraction of energy per unit time.

Question 15

If a mass-spring system oscillates with amplitude $$A$$ and angular frequency $$\omega$$, what is the maximum speed $$v_{max} of $$the mass?

Accepted Answer

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

Oscillations and Waves: Study Notes for Physics

Study Guide - Practice Questions

Study Guide - Flashcards