Waves

JEE Main level, numerical answer, medium

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Question 5 of 142

The equation of wave is given by Y=10−2sin⁡2π(160t−0.5x+π4)Y={10}^{-2}\sin 2\pi \left(160t-0.5x+\dfrac{\pi }{4}\right), where xx and YY are in mm and tt in ss. The speed of the wave is _______ kmh−1km{h}^{-1}.

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Answer: 1152

The equation of the wave is
Y=10−2sin⁡2π(160t−0.5x+π4)Y={10}^{-2}\sin 2\pi (160t-0.5x+\dfrac{\pi }{4})
The velocity of a wave is given by v=ωk...(i)v=\dfrac{\omega }{k}...(i).
A wave equation is given by
Y=Asin⁡(ωt−kx+ϕ)Y=A\sin \left(\omega t-kx+\phi \right)
Using equation (i),
v=(2π×1602π×0.5)=320ms−1v=\left(\dfrac{2\pi \times 160}{2\pi \times 0.5}\right)=320m{{s}^{-1}}_{}
⇒v=320×185\Rightarrow v=320\times \dfrac{18}{5}
⇒v=1152kmh−1\Rightarrow v=1152km{h}^{-1}

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