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 ...........

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

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

$A$ simple harmonic progressive wave is given by $Y = Y_0 \sin 2 \pi (nt - \frac{x}{\lambda})$. If the wave velocity is $(1/8)^{\text{th}}$ of the maximum particle velocity,then the wavelength is

$A$ wave is given by $y=5 \times 10^{-3} \sin \left(12.5 \pi x - \frac{\pi}{2} t\right)$. Then its wavelength and time period are respectively ($y$ and $x$ are in metres and $t$ is in seconds).

$A$ 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: