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A transverse wave is represented by the ...

A transverse wave is represented by the equation `y = y sin (2pi)/lambda (vt -x)` For what value of `lambda` , is the maximum particle velocity equal to two times the wave velocity?

A

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

B

`lambda = (pi y_(0))/3`

C

`lambda = 2pi y_(0)`

D

`lambda = pi y_(0)`

Text Solution

Verified by Experts

The correct Answer is:
D
The given equation of wave is:
`y =y_(0)sin (2pi)/lambda (vt -x)`
Particle velocity `=(dy)/(dt) = y_(0)cos (2pi)/lambda (vt-x) .(2piv)/lambda`
`((dy)/(dt))_("max") = y_(0).(2pi)/lambda v`
`therefore y_(0) =(2pi)/lambda v =2 v` or `lambda = pi y_(0)`
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