Q: A mass $$m is $$launched vertically from Earth's surface with speed $$v. $$What is the minimum speed required to escape Earth's gravity (neglecting air resistance)?

$$v_{\text{esc}} = \sqrt{\frac{2GM}{R}}$$

Q: A loudspeaker emits a sound with intensity $$I_1 at 1 $$meter. What is the decibel level at this distance?

$$\beta = 10 \log_{10} \left( \frac{I_1$}{I_0$} \right)$$, where $$I_0$$ = $$10^{-12}$$ \text{W/m}^2$$

Question 1

A satellite is orbiting Earth at a distance $$r$$ from the center of the planet. According to Newton's law of universal gravitation, what is the magnitude of the gravitational force acting on the satellite?

Accepted Answer

$$F = \frac{G m_1$ m_2$}{r^2$}$$

Question 2

A mass $$m$$ attached to a spring with spring constant $$k$$ undergoes simple harmonic motion. What is the period $$T of $$the oscillation?

Accepted Answer

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

Question 3

A pendulum clock is taken from Earth to the Moon, where the acceleration due to gravity is lower. What happens to the period of the pendulum?

Accepted Answer

The period increases because $$T = 2\pi \sqrt{\frac{L}{g}}$$ and $$g is $$smaller on the Moon.

Question 4

A mass-spring system oscillates with amplitude $$A. $$What is the total mechanical energy of the system?

Accepted Answer

$$E = \frac{1}{2} k A^2$

Question 5

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

Accepted Answer

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

Question 6

A car horn emits a sound of frequency $$f_0 as it $$approaches a stationary observer. According to the Doppler effect, what frequency $$f$$ does the observer hear?

Accepted Answer

$$f = f_0$ \left( \frac{v + v_o}{v - v_s} \right)$$, with $$v_o = 0$$ and $$v_s$$ positive toward observer

Question 7

A string fixed at both ends has length $$L. $$What is the wavelength of the fundamental mode (first harmonic) of standing waves on the string?

Accepted Answer

$$\lambda = 2L$$

Question 8

A pipe open at both ends has length $$L. $$What is the frequency of the fundamental mode, given the speed of sound $$v$$?

Accepted Answer

$$f_1$$ = \frac{v}{2L}$$

Question 9

A mass $$m is $$dropped from a height $$h$$ above the surface of the Earth. What is its gravitational potential energy relative to the surface?

Accepted Answer

$$U = mgh$$

Question 10

A person shouts and the sound intensity at a distance of 2 meters is $$I_0. $$What is the sound intensity at a distance of 4 meters, assuming spherical spreading and no absorption?

Accepted Answer

$$I = \frac{I_0$}{4}$$

Question 11

A mass $$m$$ attached to a spring oscillates with angular frequency $$\omega. If $$the mass is doubled, what happens to the angular frequency?

Accepted Answer

It decreases: $$\omega = \sqrt{\frac{k}{m}}$$, so doubling $$m$$ makes $$\omega$$ decrease by $$\frac{1}{\sqrt{2}}.$$

Question 12

A tuning fork produces a sound at 440 Hz. If another fork produces a sound at 442 Hz, what is the beat frequency heard when both are sounded together?

Accepted Answer

2 Hz

Question 13

A mass $$m is $$launched vertically from Earth's surface with speed $$v. $$What is the minimum speed required to escape Earth's gravity (neglecting air resistance)?

Accepted Answer

$$v_{	ext{esc}} = \sqrt{\frac{2GM}{R}}$$

Question 14

A damped oscillator loses energy over time. Which of the following best describes the effect of damping on the amplitude of oscillation?

Accepted Answer

The amplitude decreases exponentially with time.

Question 15

A child swings on a playground swing (a simple pendulum). If the child increases the length of the swing, what happens to the period?

Accepted Answer

The period increases because $$T = 2\pi \sqrt{\frac{L}{g}}.$$

Question 16

A string vibrates in its third harmonic. How many nodes (excluding the ends) are present?

Accepted Answer

2 nodes

Question 17

A physical pendulum consists of a rigid rod of length $$L$$ pivoted at one end. What is the period of small oscillations?

Accepted Answer

$$T = 2\pi \sqrt{\frac{I}{mgd}}$$

Question 18

Two speakers emit sound waves of the same frequency and amplitude in phase. At a point equidistant from both, what type of interference occurs?

Accepted Answer

Constructive interference

Question 19

A wave travels along a string with linear mass density $$\mu$$ and tension $$T. $$What is the speed of the wave?

Accepted Answer

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

Question 20

A loudspeaker emits a sound with intensity $$I_1 at 1 $$meter. What is the decibel level at this distance?

Accepted Answer

$$\beta = 10 \log_{10} \left( \frac{I_1$}{I_0$} ight)$$, where $$I_0$$ = $$10^{-12}$$ 	ext{W/m}^2$$

Physics 1500 Final Exam Study Guide: Gravitation, Oscillations, and Waves

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