Figure shows a snapshotof 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= 0at t = 0, write theequation of travelling wave. ,

Figure shows a snapshotof a sinusoidal travelling wave taken at t= 0.3

1.	Figure shows a snapshotof 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= 0at t = 0, write theequation of travelling wave. ,
Answer» Solution :Given, `A = 2 cm, LAMBDA=7.5 cm` `:. k=(2pi)/(lambda)=0.84 cm^(-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) = 4 cm//s` `:.` ANGULAR frequency `omega=(v)/(k)=3.36 rad//s` Since the wave is travelling along positive X-directionand crest (maximum displacement) is at `x = 0` at `t= 0` , we can write the wave equation as `y(x, t)=A cos (kx -OMEGAT)` or `y(x, t)= A cos (omegat -kx)`as`cos(- theta)= cos theta` Therefore, the desired equation is `y(x, t) = (2 cm) cos [(0.84 cm^(-1) x - (3.36 rad//s)t] cm`