Question 1

A mass $$m$$ attached to a spring with spring constant $$k$$ oscillates with simple harmonic motion (SHM). If the amplitude of oscillation is doubled, what happens to the maximum kinetic energy of the mass?

Accepted Answer

It increases by a factor of 4.

Question 2

Which of the following is the correct differential equation for the position $$x(t) of a $$mass-spring system undergoing simple harmonic motion?

Accepted Answer

$$m \frac{d^2$x}{dt^2$} + kx = 0$$

Question 3

A pendulum of length $$L$$ swings with small amplitude. Which expression gives its period $$T$$?

Accepted Answer

$$T = 2\pi \sqrt{\frac{L}{g}}$$

Question 4

A damped oscillator is described by $$x(t) = A e$$^{-bt/2m}$$ \cos(\omega' t + \phi). $$What does the parameter $$b$$ represent?

Accepted Answer

The damping coefficient

Question 5

A child pushes a swing periodically, matching the swing's natural frequency. This is an example of:

Accepted Answer

Resonance

Question 6

A sound wave travels through air at $$v = 343\ \mathrm{m/s}. If $$its frequency is $$f = 686\ \mathrm{Hz}$$, what is its wavelength $$\lambda$$?

Accepted Answer

$$\lambda = 0.5\ \mathrm{m}$$

Question 7

Which of the following best describes a transverse wave?

Accepted Answer

The medium moves perpendicular to the direction of wave propagation.

Question 8

A stationary observer hears a sound from a moving source. If the source moves toward the observer, what happens to the frequency heard by the observer?

Accepted Answer

It increases.

Question 9

Which equation gives the observed frequency $$f_o$$ for a stationary observer and a source moving toward the observer at speed $$v_s ($$sound speed $$v$$)?

Accepted Answer

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

Question 10

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

Accepted Answer

A standing wave

Question 11

For a string fixed at both ends, which of the following is true for the fundamental mode (first harmonic)?

Accepted Answer

There is one antinode and two nodes.

Question 12

Which of the following best describes constructive interference?

Accepted Answer

Two waves meet and their amplitudes add.

Question 13

A spherical wavefront expands from a point source. What happens to the intensity as the distance from the source doubles?

Accepted Answer

It decreases by a factor of 4.

Question 14

A mass on a spring oscillates with $$x(t) = A \cos(\omega t + \phi). $$What is the velocity $$v(t)$$?

Accepted Answer

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

Question 15

Which of the following statements about resonance is correct?

Accepted Answer

Resonance occurs when the driving frequency matches the natural frequency.

Question 16

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

Accepted Answer

$$v = \frac{\omega}{k}$$

Question 17

If the path difference between two waves is $$\Delta r = n \lambda$$, what type of interference occurs?

Accepted Answer

Constructive interference

Question 18

A car horn emits a frequency $$f as it $$approaches a stationary observer. The observer hears a frequency $$f_o$$ higher than $$f. $$Which effect explains this?

Accepted Answer

Doppler effect

Question 19

Which of the following is true for the energy in simple harmonic motion (SHM)?

Accepted Answer

Total energy is constant and equals $$\frac{1}{2} k A^2$

Oscillations, Waves, and Superposition: Study Guide for Physics 163

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