Figure shows a snapshot of a sinusoidal travelling wave taken at  $t=0.3s.$  The wavelength is 7.5 cm and amplitude is 2 cm.  If the crest $P$  was at  $x=0$ at $t=0,$  write the equation of travelling wave.

Given,  $A=2cm,\lambda =7.5cm$
$k=\frac{2\pi }{\lambda }=\frac{4\pi }{15}c{m}^{-1}$
The wave has travelled a distance of 1.2 cm in 0.3 s.  Hence, speed of the wave,  $v=1.2/0.3=4cm/s$
Therefore, angular frequency  $\omega =\left(v\right)\left(k\right)=\frac{16\pi }{15}rad/s$
Since the wave is travelling along positive x-direction and crest (maximum displacement) is at $x=0$  at $t=0,$   we can write the wave equation as,  
$y(x,t)=2\cos (kx-\omega t)=2\cos (\frac{4\pi }{15}x-\frac{16\pi }{15}t)$