In the wave equation $y = 0.5 \sin \frac{2 \pi}{\lambda}(400 t - x ) \, m$,the velocity of the wave will be ......... $m/s$.

$A$ transverse sinusoidal wave of amplitude '$a$',wavelength $\lambda$,and frequency $f$ is travelling on a stretched string. The maximum speed at any point on the string is $v/10$,where $v$ is the speed of propagation of the wave. If $a = 10^{-3} \ m$ and $v = 10 \ ms^{-1}$,then $\lambda$ and $f$ are given by:

$A$ travelling wave is described by the equation $y(x, t) = 0.05 \sin(8x - 4t) \; m$. The velocity of the wave is $..... \; m/s$ [all the quantities are in $SI$ units].

The equation of a wave is represented by $y = 10^{-4} \sin(100t - x/10)$. The velocity of the wave will be .... $m/s$.

The equation of a longitudinal wave is represented as $y = 20 \cos \pi (50t - x)$. Its wavelength is ..... $cm$.

The transverse displacement $y(x, t)$ of a wave on a string is given by $y(x, t) = e^{-(ax^2 + bt^2 + 2\sqrt{ab}xt)}$. This represents a