Answer to Question #122627 in Optics for Naineshwari

Question #122627
find wave velocity when in shm when y=0.25cos (125t- 0.25x)
1
Expert's answer
2020-06-17T09:10:07-0400

We are assuming all the quantities are in S.I.

Wave equation is

y=0.25cos(125t0.25x)=0.25sin(0.25x125t+π)y=0.25\cos(125t-0.25x)=0.25\sin(0.25x-125t+\pi)

Now,

k=0.25    λ=2π0.25=8πk=0.25\implies \lambda=\frac{2\pi}{0.25}=8\pi

And,

2πvwλ=125    vw=1254=500m/s\frac{2\pi v_w}{\lambda}=125\implies v_w=125\cdot4=500m/s


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