Waves practice · Mixed difficulty

Two sound waves are represented by $y = a\,\,\sin \left( {\omega t - kx} \right)$ and $y = a\,\,\cos \left( {\omega t - kx} \right)$. The wavelength of waves in water are

In the first overtone position of the resonance tube, the pressure anti-node is present at (L is the length of the tube) which positions from the closed end.

If $T$ is the reverberation time of an auditorium of volume $V$ then

${v_1}\, and \,{v_2}$ are the velocities of sound at the same temperature in two monoatomic gases of densities ${\rho _1}$ and ${\rho _2}$ respectively. If ${\rho _1}/{\rho _2} = \frac{1}{4}$ then the ratio of velocities ${v_1}{\mkern 1mu} \,\,and\,\,{\mkern 1mu} {v_2}$ will be

Tuning fork ${F_1}$ has a frequency of $256\,\,Hz$ and it is observed to produce $6\mathrm{ }beats/second$ with another tuning fork ${F_2}$. When ${F_2}$ is loaded with wax, it still produces $6\mathrm{ }beats/second$ with ${F_1}$. The frequency of ${F_2}$ before loading was

Beats are produced by two travelling waves each of loudness $I$ and nearly equal frequencies ${n_1}$ and ${n_2}$. The beat frequency will be and maximum loudness hard will be

The frequency and velocity of sound wave are $600\,\,Hz\,\,\,and\,\,\,360\,\,m/s$ respectively. Phase difference between two particles of medium are $60^\circ$, the minimum distance between these two particles will be

A source emits a sound of frequency of $400\,\,Hz$, but the listener hearts its $390\,\,Hz$. Then

A sound source of constant frequency resonates with an open end organ pipe of length $30 \mathrm{~cm}$ and a close end organ pipe of length $23 \mathrm{~cm}$ (both of same diameter). Both pipes are sounding their first overtone. If velocity of sound is $340 \mathrm{~ms}^{-1}$, then find the end correction in $\mathrm{cm}$.

The equation of a transverse wave is given by $y = 10\sin \pi (0.01x - 2t)$ where x and y are in cm and t is in second. Its frequency is

What is the phase difference between two successive crests in the wave?

Velocity of sound is maximum in

Statement-I: In longitudinal progressive waves, when the particle is at the mean position, it is a region of maximum compression or rarefaction.
Statement-II: In longitudinal progressive waves, compressions and rarefactions travel forward along the wave.

If in a resonance tube a oil of density higher than that water is used then at the resonance frequency would

Statement I: Sonometer is used to determine frequency of unknown T.F.

Statement II: In sonometer riders used as indicator.

The displacement of a particle executing periodic motion is given by $y = 4\,\,{\cos ^2}\left( {t/2} \right)\,\,\,\sin \,\,\left( {1000\,t} \right)$. This expression may be considered to be a result of superposition of

The fourth overtone of an open organ pipe has the same frequency as the second overtone of a close pipe of length L. The length of open pipe will be.

A wave length 0.6 cm is produced in air and it travels at a speed of 300 m/s. it will be an

A closed organ pipe and an open organ pipe of the same length produce four beats, when sounded together. If the length of the closed organ pipe is increased then the number of beats will

A wave travelling along a string is described by the equation $y = a\sin \left( {\omega t - kx} \right)$ the maximum particle velocity is

A tuning fork of known frequency $256\,\,Hz$ makes $5\,\,beats/s$ with the vibrating string of a piano. The beat frequency decreases to $2\,\,beats/s$ when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was

The mathematical form of three travelling waves are given by

$\begin{aligned} & y_1=(2 {~cm}) \sin (3 x-6 t), \\ & y_2=(3 {~cm}) \sin (4 x-12 t) \text {, } \\ & \text { and } y_3=(4 {~cm}) \sin (5 x-11 t) \\ \end{aligned}$

of these waves,

Two open pipes of length L are vibrated simultaneously. If length of one of the pipe is reduced by y, then the number of beats heard per second will be. (if the velocity of sound is V and y < < L)

From a point source, if amplitude of waves at a distance $r$ is A, its amplitude at a distance $2r$ will be

An open tube is in resonance with a string. If tube is dipped in water, so that 75% of length of the tube is inside water, then ratio of frequency of tube to string is

The equation of a spherical progressive wave is

A tuning fork gives $5$ beats with another tuning fork of frequency $100\,\,Hz.$ When the first tuning fork is loaded with wax, then the number of beats remains unchanged, then what will be the frequency of the first tuning fork

A wave travelling along positive $x$-axis is given by $y = A\sin \left( {\omega t - kx} \right)$. If it is reflected from rigid boundary such that $80\%$ amplitude is reflected, then equation of reflected wave is

Statement I Two longitudinal waves given by equation ${y_1}\left( {x,t} \right) = 2a\,\,\,\sin \left( {\omega t - kx} \right)$ and ${y_2}\left( {x,t} \right) = a\,\,\sin \left( {2\omega t - 2kx} \right)$ will have equal intensity.
Statement II Intensity of waves of given frequency in same medium is proportional to square of amplitude only

Two tuning forks of frequency ${n_1}$ and ${n_2}$ produces n beats per second. If ${n_2}$ and n are known, ${n_1}$ may be given by