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 $m/s$)

$A$ wave equation which gives the displacement along $y$-direction is given by $y = 0.001 \sin(100t + x)$,where $x$ and $y$ are in meters and $t$ is time in seconds. This represents a wave:

Obtain the relation between wave velocity,angular frequency,and angular wave number.

$A$ transverse wave of frequency $500 \,Hz$ and speed $100 \,m/s$ is travelling in the positive $x$-direction on a long string. At time $t=0 \,s$,the displacements at $x=0.0 \,m$ and at $x=0.25 \,m$ are $0.0 \,m$ and $0.02 \,m$,respectively. The displacement at $x=0.2 \,m$ at $t=5 \times 10^{-4} \,s$ is ............ $m$.

When a sound wave of wavelength $\lambda$ is propagating in a medium,the maximum velocity of the particle is equal to the wave velocity. The amplitude of the wave is:

The equation of a travelling wave is $y = a \sin 2 \pi (p t - \frac{x}{5})$. Then the ratio of the maximum particle velocity to the wave velocity is ...........