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. `(piA)/2`
B. `piA`
C. `2piA`
D. A

Answer

C

Explanation

The given wave equation is,y=Asin`(omegat-kx)`
Wave velocity,`v=omega/k`….(i)
Particle velocity,`v_(p)=(dy)/(dt)=Aomegacos(omegat-kx)`
Maximim particle velocity, `(v_(p))_(max)`
`omega/k=Aomega` (Using (i) and (ii))
`1/k=Aorlamda/(2pi)=A`(`becausek=(2pi)/lamda`)
`lamda=2piA`