Waves practice · Medium

The speed of propagation of a wave in a medium is $300 \mathrm{~m} / \mathrm{s}$. The equation of motion of point at $x=0$ is given by $y=0.04 \sin 600 \pi t$ (metre). The displacement of a point $x=75 \mathrm{~cm}$ at $t=0.01 \mathrm{~s}$ is

A person blows into the open end of a long pipe. As a result, a high-pressure pulse of air travels down the pipe. When this pulse reaches the other end of the pipe,

A plane wave is described by the equation $y = 3\cos \left( {\frac{x}{4} - 10t - \frac{\pi }{2}} \right)$. The maximum velocity of the particles of the medium due to this wave is

Two transverse sinusoidal waves travel in opposite directions along a string. The speed of transverse waves in the string is $0.5 \mathrm{~cm} \mathrm{~s}^{-1}$. Each has an amplitude of $3.0 \mathrm{~cm}$ and wavelength of $6.0 \mathrm{~cm}$. The equation for the resultant wave is

Assertion (A) : If we see the oscillations of a stretched wire at higher overtone mode, frequency of oscillation increases but wavelength decreases.

Reason (R) : From $v=f \lambda, \lambda \propto \frac{1}{f}$ as $v=$ constant.

The relation between frequency $n$, wavelength $\lambda$ and velocity $v$ of propagation of wave is

Sound travels in rocks in the form of:

Two tuning forks of frequency 250 Hz and 256 Hz produce beats. Then beat frequency is

When a wave travelling from one medium is
refracted into other medium, which of the
following will not change?

A listener is at rest with respect to the source of sound. A wind start blowing along the line joining the source and the observer. Which of the following quantities do not change?

Two periodic waves of amplitudes $a$ and $b$ pass through a region at the same time in the same direction. If $a > b$, the difference in the maximum and minimum possible amplitudes is

A $100 \mathrm{~Hz}$ sinusoidal wave is travelling in the positive $x$-direction along a string with a linear mass density of $3.5 \times 10^{-3} \mathrm{~kg} / \mathrm{m}$ and a tension of $35 \mathrm{~N}$. At time $t=0$, the point $x=0$, has maximum displacement in the positive $y$-direction. Next when this point has zero displacement, the slope of the string is $\pi / 20$. Which of the following expression represent (s) the displacement of string as a function of $x$ (in metre) and $t$ (in second)

Out of the given waves (1), (2), (3) and (4)
$y = a\sin \left( {kx + \omega t} \right)$ ...($1$)
$y = a\sin \left( {\omega t - kx} \right)$ …($2$)
$y = a\cos \left( {kx + \omega t} \right)$ …($3$)
$y = a\cos \left( {\omega t - kx} \right)$ …($4$)
Emitted by four different sources ${S_1},{S_2},{S_3}\,\,and\,\,{S_4}$ respectively, interference phenomena would be observed in space under appropriate conditions when

A string of length $2 \mathrm{x}$ is stretched by $0.1 \mathrm{x}$ and the velocity of a transverse wave along it is $v$. When it is stretched by $0.4 \mathrm{x}$ the velocity of the wave is