Questions

The displacement y of a particle in a medium can be expressed as $y = 10^{- 6} \sin (100 t + 20 x + \frac{x}{4})$ , where
t is in second and x in metre. The speed of the wave is

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2000 ms-1

5 ms-1

20 ms-1

5π ms-1

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detailed solution

Correct option is B

The displacement is given by y=10−6sin⁡100t+20x+π4Comparing with standard equation y=Asin⁡(ωt+kx+ϕ)we get ω=100,k=20where, ω is angular frequency and k is angular wave number.Now, k=2πλ=2πvλv=ωv=20⇒ v=ω20=10020=5ms−1So, the speed of the wave is 5 ms-1.

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