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Shows a snapshot of a sinusoidal travell...

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.

Text Solution

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Given ,`A=2 cm,lambda=7.5 cm`
`k=(2pi)/(lambda)=(4pi)/(15)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`
Therefore, angular frequency `omega=(v)(k)`
`=(16pi)/(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-omegat)`
`=2 cos((4pi)/(15)x-(16pi)/(15)t)`
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