What is the phase difference between consecutive crest and trough?

Obtain the relation between wave velocity,angular frequency,and angular wave number.

If the equation of a progressive wave is given by $y = 3 \cos \pi (100 t - x) \text{ cm}$,then what is the wavelength of the wave in $\text{cm}$?

$A$ transverse wave is travelling along a string from left to right. The adjoining figure represents the shape of the string at a given instant. At this instant,among the following,choose the wrong statement.

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:
$(a)$ $(x-vt)^2$
$(b)$ $\log[(x+vt)/x_0]$
$(c)$ $1/(x+vt)$

$A$ wave is represented by the equation $y = 0.5 \sin(10t - x) \ m$. It is a travelling wave propagating along the $+x$ direction with velocity .... $m/s$.