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A travelling wave is described by the eq...

A travelling wave is described by the equation `y = y_(0) sin2 pi ((ft - (x)/lambda))`. The maximum particle velocity is equal to four times the wave velocity if

A

`lamda=pi(y_(0))/(4)`

B

`lamda=pi(y_(0))/(2)`

C

`lamda=piy_(0)`

D

`lamda=2piy_(0)`

Text Solution

Verified by Experts

The correct Answer is:
B
`y=y_0 sin2pi[ft-x/lambda] therefore dy/dt=[y_0cos 2pi(ft-x/lambda)]xx2pi f implies[dy/dt]_max=y_0xx2xf`
Given that maximum particle velocity is equal to four times the wave velocity `(c=lambda)`
`therefore y_0xx2pi f=4 fxxlambda,lambda=(piy_0)/2`
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Knowledge Check

  • A transverse wave is described by the equatiion Y = Y_(0) sin 2pi (ft -x//lambda) . The maximum particle velocity is equal to four times the wave velocity if lambda = pi Y_(0) //4 lambda = pi Y_(0)//2 lambda = pi Y_(0) lambda = 2pi Y_(0)

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