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A transverse wave in a medium is describ...

A transverse wave in a medium is described by the equation ` y = A sin 2(omegat - kx)` . The magntiude of the maximum velocity of particles in the medium is equal that of the of the wave velocity . If the value of A is

A

` lambda/(2pi)`

B

`lambda/(4 pi) `

C

`lambda/pi`

D

`(2lambda)/pi`

Text Solution

Verified by Experts

The correct Answer is:
B
The given equation of the transverse wave is ` y= A sin2 ( omegat -kx)`
Velocity of the particle = ` (dy)/(dt) = 2 A omegacos 2 (omegat - kx) `
Maximum velocity ` = 2 A omega`
Velocity of the wave = ` ("Coefficient of t ")/( "Coefficient of x ") = (2 Omega)/(2kg) = Omega/k`
As per question
` 2 A omega = omega/k or 2A = 1/k = lamda/(2pi) Rightarrow A = lamda/(4pi)`
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