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Question

The transverse wave propagating through a medium is given by $$y=A\cos { 2\pi  } \left[ ft-\cfrac { x }{ \lambda  }  \right] $$. If maximum particle velocity of medium is two times the velocity of wave through medium, then.


A
λ=3.14A
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B
λ=6.28A
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C
6.28λ=A
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D
3.14λ=A
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Solution

The correct option is A $$\lambda =3.14A$$

Velocity of a particle

$$ {{v}_{p}}=\nu \lambda  $$

$$ {{v}_{p}}=A\omega  $$

$$ =A2\pi \nu .....(1) $$

Maximum velocity of a wave $${{v}_{g}}=\nu \lambda ............(2)$$

It is given that $${{v}_{p}}=2{{v}_{g}}$$

Using equation (1) and (2)

$$ A2\pi \nu =2\nu \lambda  $$

$$ \lambda =\pi A $$

$$ \lambda =3.14\,A $$



Physics

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