$A$ wave is represented by the equation: $y = a \sin(0.01x - 2t)$,where $a$ and $x$ are in $cm$. The velocity of propagation of the wave is .... $cm/s$.

For the travelling harmonic wave $y(x, t) = 2.0 \cos 2 \pi(10 t - 0.0080 x + 0.35)$,where $x$ and $y$ are in $cm$ and $t$ is in $s$. Calculate the phase difference between oscillatory motion of two points separated by a distance of:
$(a)$ $4 \, m$
$(b)$ $0.5 \, m$
$(c)$ $\lambda / 2$
$(d)$ $3 \lambda / 4$

The equation of a progressive wave is $y = 8 \sin \left[ \pi \left( \frac{t}{10} - \frac{x}{4} \right) + \frac{\pi}{3} \right]$. The wavelength of the wave is .... $m$.

What will be the change in phase of a wave due to reflection from a free support?

$A$ wave is represented by the equation $y = 7\sin \{ \pi (2t - 2x) \} $ where $x$ is in metres and $t$ is in seconds. The velocity of the wave is ..... $m/s$.

In a transverse wave,the distance between a crest and the neighbouring trough at the same instant is $4.0 \, cm$,and the distance between a crest and trough at the same place is $1.0 \, cm$. The next crest appears at the same place after a time interval of $0.4 \, s$. The maximum speed of the vibrating particles in the medium is