$A$ transverse wave is described by the equation $y = y_0 \sin 2 \pi \left( \nu t - \frac{x}{\lambda} \right)$. The maximum particle velocity is equal to four times the wave velocity if $\lambda =$

An observer on a sea-coast counts $45$ waves in one minute. If the wavelength of the waves is $7 \ m$,then the velocity of the waves will be (in $m/s$)

Write the definition of wave speed and its $SI$ unit.

When two sound waves travel in the same direction in a medium,the displacements of a particle located at $x$ at time $t$ are given by:
$y_1 = 0.05 \cos(0.50 \pi x - 100 \pi t)$
$y_2 = 0.05 \cos(0.46 \pi x - 92 \pi t)$
Then the velocity of the waves is..... $m/s$.

In a transverse wave,the distance between a crest and the neighbouring trough at the same instant is $4.0 \, cm$,and the distance between a crest and trough at the same place is $1.0 \, cm$. The next crest appears at the same place after a time interval of $0.4 \, s$. The maximum speed of the vibrating particles in the medium is

The disturbance $y(x, t)$ of a wave propagating in the positive $x$-direction is given by $y = \frac{1}{1 + x^2}$ at time $t = 0$ and by $y = \frac{1}{1 + (x - 1)^2}$ at $t = 2 \ s$,where $x$ and $y$ are in meters. The shape of the wave disturbance does not change during the propagation. The velocity of the wave in $m/s$ is: