Q: A sound wave in air has a frequency of 500 Hz and a wavelength of 0.68 m. What is the speed of sound in air?

$v = f \lambda = 500 \times 0.68 = 340$ m/s

Question 1

A mass $m$ attached to a spring with spring constant $k$ oscillates with amplitude $A$. What is the angular frequency $\omega$ of the oscillation?

Accepted Answer

$\omega = \sqrt{\frac{k}{m}}$

Question 2

A 0.5 kg mass oscillates on a spring with $k = 200$ N/m. What is the period $T$ of oscillation?

Accepted Answer

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

Question 3

Which of the following best describes the energy in a simple harmonic oscillator?

Accepted Answer

The total mechanical energy is constant and is given by $E = \frac{1}{2}kA^2$

Question 4

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 5

A string of length $L$ and mass $m$ is under tension $T$. What is the speed of transverse waves on the string?

Accepted Answer

$v = \sqrt{\frac{T}{\mu}}$, where $\mu = \frac{m}{L}$

Question 6

Which of the following statements about standing waves on a string fixed at both ends is correct?

Accepted Answer

The allowed wavelengths are $\lambda_n = \frac{2L}{n}$, where $n = 1, 2, 3, ...$

Question 7

A sound wave in air has a frequency of 500 Hz and a wavelength of 0.68 m. What is the speed of sound in air?

Accepted Answer

$v = f \lambda = 500 	imes 0.68 = 340$ m/s

Question 8

The intensity $I$ of a wave is proportional to which of the following?

Accepted Answer

$I \propto A^2$

Question 9

A tube open at both ends has length $L$. What is the fundamental frequency $f_1$ of the standing sound wave in the tube?

Accepted Answer

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

Question 10

Two sound waves of frequencies $f_1 = 440$ Hz and $f_2 = 444$ Hz interfere. What is the beat frequency?

Accepted Answer

$f_b = |f_1 - f_2| = 4$ Hz

Question 11

A standing wave is formed by the superposition of two waves traveling in opposite directions. If the incident wave is $y_1(x, t) = A \sin(kx - \omega t)$ and the reflected wave is $y_2(x, t) = A \sin(kx + \omega t)$, what is the resulting standing wave?

Accepted Answer

$y(x, t) = 2A \sin(kx) \cos(\omega t)$

Question 12

The speed of sound in a gas is given by $v = \sqrt{\gamma \frac{P}{\rho}}$. What does $\gamma$ represent?

Accepted Answer

$\gamma$ is the adiabatic index (ratio of heat capacities)

Question 13

A string of length $L$ and mass $m$ is under tension $T$. If the tension is quadrupled, how does the fundamental frequency $f_1$ change?

Accepted Answer

It doubles: $f_1 \propto \sqrt{T}$

Question 14

A sound wave in water has an intensity of $I = 1.0 	imes 10^{-3}$ W/m$^2$. If the intensity level in decibels is $\beta = 10 \log_{10}(I/I_0)$, where $I_0 = 1.0 	imes 10^{-12}$ W/m$^2$, what is $\beta$?

Accepted Answer

$\beta = 90$ dB

Question 15

Which of the following is true for a longitudinal wave in a gas?

Accepted Answer

The oscillations of the particles are parallel to the direction of wave propagation

Question 16

A tube closed at one end and open at the other has length $L$. What is the wavelength of the fundamental mode?

Accepted Answer

$\lambda_1 = 4L$

Question 17

A 200 g mass attached to a horizontal spring oscillates at a frequency of 2 Hz. What is the angular frequency $\omega$?

Accepted Answer

$\omega = 4\pi$ rad/s

Question 18

Which of the following best describes resonance in a forced oscillator?

Accepted Answer

The amplitude of oscillation is maximized when the driving frequency matches the natural frequency

Question 19

Two speakers emit sound waves of the same frequency and amplitude in phase. At a certain point, the path difference between the waves is $\lambda/2$. What is observed at this point?

Accepted Answer

Destructive interference (minimum intensity)

Oscillatory Motion and Mechanical Waves: Study Notes

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