A simple harmonic wave is represent by the relation
`y(x,t)=a_(0) sin 2pi(vt-(x)/(lambda))`
if the maximum particle velocity is three times the wave velocity, the wavelength `lambda` of the wave is

Options

A. `pi a_(0)//3`
B. `2pia_(0)//3`
C. `pia_(0)`
D. `pi a_(0)//2`

Answer

b

Explanation

Maximum particle velocity `=a_(0)omega=2pi a_(0)v`
Wave velocity`=vlambda`
Given that `2pi a_(0) v=3v lambda`
or `lambda=(2pi a_(0)//3)`