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Figure shows a snapshot of a sinusoidal...

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. ,

Text Solution

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The correct Answer is:
A, B, C, D
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-direction and 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`
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