Waves

JEE Main level, single correct, medium

42 of 142

Question 42 of 142

A standing wave is formed by the superposition of two waves travelling in opposite directions. The transverse displacement is given by, y(x,t)=0.5sin⁡⁡(5π4x)cos⁡⁡(200πt)y\left(x,t\right)=0.5\sin ⁡\left(\dfrac{5\pi }{4}x\right)\cos ⁡\left(200\pi t\right). What is the speed of the travelling wave moving in the positive xx direction? (xx and ttare in meter and second, respectively)

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Answer: (C) 160ms−1160m{s}^{-1}

y=2asin⁡(kx)cos⁡(ωt)y=2a\sin \left(kx\right)\cos \left(\omega t\right)

⇒k=5π4m−1,ω=200πrads−1\Rightarrow k=\dfrac{5\pi }{4}{m}^{-1},\omega =200\pi rad{s}^{-1},

v=ωkv=\dfrac{\omega }{k}=200π5π4=160ms−1=\dfrac{200\pi }{\dfrac{5\pi }{4}}=160m{s}^{-1}

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