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A transverse wave is described by the eq...

A transverse wave is described by the equation `y= A sin 2 pi (vt - x/lambda)`. The maximum particle velocity is equal to four times the wave velocity if

A

`lambda=(pi A)/4`

B

`lambda=(pi A)/2`

C

`lambda = piA`

D

`lambda =2 pi A`

Text Solution

Verified by Experts

The correct Answer is:
B
Given, `y=A sin 2pi (vt-x/lambda)`,
Wave velocity `=v lambda` ...(i)
Particle velocity `=(dy)/(dt)=(2 pi v A) cos 2 pi (vt-x/lambda)`
Maximum particle velocity `= 2pi v A` ...(ii)
Given, the maximum particle velocity is equal to four times the wave velocity.
`:. 2 pi v A=4 xx (v lambda)` or `lambda =(pi A)/2`
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