$A$ 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

The equation $y = A \cos^2 \left( 2\pi nt - 2\pi \frac{x}{\lambda} \right)$ represents a wave with

In a sinusoidal wave,the time required for a particular point to move from maximum displacement to zero displacement is $0.170\,s$. The frequency of the wave is .... $Hz$.

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 phase difference between two waves represented by $y_1 = 10^{-6} \sin [100t + (x/50) + 0.5] \, m$ and $y_2 = 10^{-6} \cos [100t + (x/50)] \, m$,where $x$ is expressed in meters and $t$ is expressed in seconds,is approximately .... $rad$.

$A$ transverse wave is represented by $y = 2 \sin(\omega t - kx) \ cm$. The value of wavelength (in $cm$) for which the wave velocity becomes equal to the maximum particle velocity is: