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

Explanation

Given, `A=2cm, lambda= 7.5 cm`
`:. K =(2pi)/lambda = 0.84 cm^(-1)`

The wave has travelled a distance of 1.2 cm in 0.3s.
Hence, speed ofthe wave, ` v =1.2/0.3 = 4 cm//s`
`:.` Angular frequency `omega =(v)(k) = 3.36 red//s`
Since the wave is travelling along positive x-direction andcrest (maximum displacement) is at x = 0 at t = 0, we can write the wave equation as,
`y = A sin (kx - omegat + pi/2) (or ) y (x,t) = A cos (kx- omegat)`
`y (x,t) = (2 cm) cos [0.84cm^(-1)x -(3.36 rad//s)t] cm`