$A$ body sends waves $100 \, mm$ long through medium $A$ and $0.25 \, m$ long in medium $B$. If the velocity of waves in medium $A$ is $80 \, cm s^{-1}$,the velocity of waves in medium $B$ is .... $m s^{-1}$.

$A$ transverse wave is represented by the equation $y = y_0 \sin \frac{2\pi}{\lambda} (vt - x)$. For what value of $\lambda$ is the maximum particle velocity equal to two times the wave velocity?

The equation of a simple harmonic wave is given as $y = 5 \sin \frac{\pi}{2}(100t - x)$,where $x$ and $y$ are in meters and time $t$ is in seconds. The period of the wave is: (in $s$)

You have learnt that a travelling wave in one dimension is represented by a function $y=f(x, t)$ where $x$ and $t$ must appear in the combination $x-vt$ or $x+vt$,i.e.,$y=f(x \pm vt)$. Is the converse true? Examine if the following functions for $y$ can possibly represent a travelling wave:
$(a)$ $(x-vt)^2$
$(b)$ $\log[(x+vt)/x_0]$
$(c)$ $1/(x+vt)$

$A$ plane wave $y=a \sin (\omega t-k x)$ propagates through a stretched string. The particle velocity versus $x$ graph at $t=0$ 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 .... $rad$.