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

The amplitude of a wave represented by the displacement equation $y = \frac{1}{\sqrt{a}} \sin \omega t \pm \frac{1}{\sqrt{b}} \cos \omega t$ will be

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:

The equation of a transverse wave is given by $y = 10\sin \pi (0.01x - 2t)$ where $x$ and $y$ are in $cm$ and $t$ is in seconds. Its frequency is .... $sec^{-1}$.

The equation of a simple harmonic wave is given by $y = 6 \sin 2 \pi (2t - 0.1x)$,where $y$ and $x$ are in $mm$ and $t$ is in seconds. The phase difference between two particles $2 \ mm$ apart at any instant is (in $^{\circ}$)

If the frequency of a wave is increased by $25 \%$,then the change in its wavelength is (medium not changed).