A transverse wave is represented by `y=Asin(omegat-kx)`. For what value of the wavelength is the wave velocity equal to the maximum particle velocity?

Options

A. `2 A pi`
B. A
C. `pi A//2`
D. `pi A`

Answer

A

Explanation

Wave velocity `upsilon = v lambda = (omega lambda)/(2pi)`
Maximum particle velocity, `upsilon = omega sqrt(A^(2) - y^(2))`
`upsilon_(max) = A omega`
For, `upsilon = upsilon_(max)`
`(omega lambda)/(2pi) = A omega`
`lambda = 2pi A`