Oscillations and Waves

In the equation $y = 5 \sin(10t)$, what is the amplitude of the motion?

At the mean position of an oscillating spring-mass system, the system possesses only:

The maximum acceleration of a particle in SHM is:

If a simple pendulum is placed in a lift falling freely under gravity, its time period will be:

The time period of a simple pendulum is $T$. If the acceleration due to gravity $g$ increases by $4\%$, the time period will:

The phase difference between the displacement and the acceleration of a particle in SHM is:

If the maximum velocity of a particle in SHM is $v_m$, what is its velocity at a displacement equal to half of its amplitude?

A particle of mass $m$ is connected to two springs $k_1$ and $k_2$ in series. If the system is horizontal and frictionless, the maximum force exerted by the springs on the support when the amplitude is $A$ is:

If the length of a simple pendulum is equal to the radius of the earth $R$, its time period is given by:

In a damped oscillation, the amplitude falls to $1/e$ of its initial value after $n$ oscillations. If the time period is $T$, the damping constant $b$ (where force $F = -bv$) is:

In SHM, the value of potential energy at $x = A/3$ is what fraction of the total energy?

The kinetic energy of a particle in SHM is maximum when the acceleration is:

If the mass of the oscillator is increased by 4 times while keeping the angular frequency and amplitude constant, the total energy:

A particle executes SHM. At what position is the magnitude of the force acting on it maximum?

A mass-spring system oscillates with a frequency $f$. If the mass is halved and the frequency is kept the same by changing the spring, the total energy for the same amplitude $A$ will:

If the period of SHM is $T$, the time taken by the particle to reach the point where $PE = Total \, Energy$ from the mean position is:

The potential energy of a particle in SHM is maximum at:

In a spring-mass system, the mass is replaced by another mass four times as large. For the same total energy, the new amplitude will be:

A particle is executing SHM. At displacement $x$, its potential energy is $U_1$ and at displacement $y$, its potential energy is $U_2$. At displacement $(x+y)$, its potential energy is:

Which of the following quantities remains constant during SHM?

The time period of a simple pendulum is $2$ s. What is its frequency?

When a person swings on a playground swing and is pushed at the right moment every time, the amplitude increases. This is an example of:

For a mass-spring system, if the spring constant $k$ is increased, the natural frequency will:

The work done by a damping force is always:

A damped harmonic oscillator consists of a mass $m$, a spring with constant $k$, and a damping mechanism with constant $b$. If the damping constant $b$ is increased while the system remains underdamped, what is the resulting effect on the angular frequency ($\omega'$) and the time period ($T$) of the oscillations?

Two damped oscillators $A$ and $B$ have the same mass and spring constant. If $A$ has a higher damping constant than $B$, then $A$ will have:

The displacement of a forced oscillator leads the driving force by a phase angle of $\pi$ when:

The power dissipation in a damped harmonic oscillator is proportional to the square of the:

For a damped oscillator, if the damping constant $b$ is such that $b^2 > 4mk$, the roots of the characteristic equation are:

The phase difference between the driving force and displacement in a forced oscillator at resonance ($\omega = \omega_0$) is:

If a wave takes $0.1\text{ s}$ to travel a distance of one wavelength, what is its frequency?

A tuning fork has a frequency of $512\text{ Hz}$. This means it completes:

The units of wavelength are the same as the units of:

Which of these is a property of wave motion?

If the equation of a wave is $y = A \sin(\omega t - kx)$, the slope of the wave at any point is given by:

The unit of wave number ($k$) is:

What happens to the wavelength of a sound wave when it enters a medium where its speed is doubled?

Which of the following describes the condition for a wave to be classified as a transverse wave?

The phase velocity of a wave is $v$. If the omega-k relationship is $\omega = ak^2$ (where $a$ is a constant), the group velocity $v_g$ is:

An open pipe is in resonance with its 3rd harmonic. If one end is suddenly closed, and the frequency of the source is adjusted to maintain the same number of nodes, the new frequency relative to the original open-pipe fundamental $f_0$ is:

The shape of a progressive wave profile at a fixed instant of time is generally:

If the angular frequency $\omega$ is $2\pi\ rad/s$, what is the frequency $f$?

What is the SI unit of displacement $y$ in the wave equation?

A wave is traveling such that its position is given by $y = 5 \sin(100t - 2x)$. What is the wave number?

The displacement of a wave is $y = A \sin(kx - \omega t + \pi/3)$. What is the displacement at $x=0$ and $t=0$?

A particle on a wave takes $0.25$ seconds to move from its mean position to the maximum displacement. What is the frequency of the wave?

A wave is represented by $y = 10 \sin(x + 5t)$. In which direction and with what speed is it moving?

A wave $y = A \sin(kx - \omega t)$ is superimposed with $y = A \sin(kx + \omega t)$. The resultant is:

Which of the following represents the correct differential equation for a wave $y(x, t)$?

A wave is represented by $y = 2 \sin(3\pi t - \pi x)$. The distance between two points having a phase difference of $30^\circ$ is:

The point in a standing wave where the amplitude is $2A$ (twice the individual wave amplitude) is the:

A stationary wave is formed. If the distance between a node and the next node is $10$ cm, what is the wavelength?

In a standing wave, what is the phase difference between two particles located in the same loop?

The ratio of frequencies of the first two overtones in a closed organ pipe is:

A sonometer wire is vibrating in its second overtone. The number of nodes and antinodes are respectively:

In a stationary wave, all particles of the medium pass through their mean position:

The length of an organ pipe is $l$. If the end correction is $e$, the effective length of a closed organ pipe is:

A standing wave is formed by the superposition of $y_1 = A \sin(kx - \omega t)$ and $y_2 = A \cos(kx + \omega t)$. The resultant amplitude at $x$ is:

A wave is reflected from a rigid boundary. The ratio of the amplitude of the reflected wave to the incident wave is $1$. The phase difference between the incident and reflected wave at the boundary is:

A string fixed at both ends has a fundamental frequency of $400 \text{ Hz}$. A point at $L/4$ from one end is held fixed. The new fundamental frequency is:

In one complete beat cycle, how many times does the sound intensity reach a minimum?

If the two sources are placed very far apart, beats are not heard clearly because:

The intensity of the sound heard during beats varies between:

To produce 3 beats per second, two tuning forks should have frequencies:

A set of 24 tuning forks is arranged in increasing order of frequencies. Each fork gives 4 beats per second with the preceding one. If the frequency of the last fork is three times that of the first, the frequency of the first fork is:

If the wavelength of two waves is $200/50$ cm and $200/51$ cm, and the velocity is 200 m/s, the number of beats per second is:

Two tuning forks when sounded together produce 5 beats per second. If the frequency of one fork is 288 Hz and the other is a pipe closed at one end of length 30 cm (velocity of sound = 360 m/s), the beat frequency between the fork and the pipe's fundamental is:

Two identical strings are under the same tension $T$. When the tension in one is increased by $2\%$, the beat frequency is 10 Hz. What is the initial frequency of the strings?

Two organ pipes, both closed at one end, have lengths $L$ and $L + \Delta L$. If the velocity of sound is $v$, the beat frequency of their fundamental notes is (assume $\Delta L \ll L$):

A set of tuning forks is arranged in ascending order of frequency. Each fork gives 8 beats/s with the next one. The last fork is an octave of the first. If there are 17 forks, what is the frequency of the 9th fork?

The shift in frequency is often called the:

If an observer moves away from a stationary source with the speed of sound ($v_o = v$), the frequency heard is:

When a source recedes from a stationary observer, the crests of the waves are:

The Doppler effect is applicable to:

The apparent frequency of sound heard by a person in a car moving at $30 \text{ m/s}$ towards a stationary factory siren of $500 \text{ Hz}$ is (Speed of sound $= 330 \text{ m/s}$):

A source $S$ moves towards a stationary observer $O$ with velocity $v_s$. A wind is blowing from the observer to the source with velocity $w$. The effective speed of sound towards the observer is:

If the source of sound is stationary and the observer is moving towards it with speed $v_{obs}$, the apparent wavelength heard by the observer is:

A source of sound and an observer are moving towards each other with same speed $v/20$. The wind is blowing with speed $v/20$ in the direction of motion of the source. The change in frequency heard by the observer is:

A person is standing on a platform. A train blowing a whistle of frequency $1000 \text{ Hz}$ approaches him with a speed of $33 \text{ m/s}$. The speed of sound is $330 \text{ m/s}$. As the train passes him, the frequency change he hears is:

A galaxy is observed to have a redshift such that a spectral line of $400 \text{ nm}$ is shifted to $600 \text{ nm}$. The speed of the galaxy relative to Earth is (using non-relativistic approximation for logic check, then relativistic):