The maximum particle velocity in a wave motion is half the wave velocity. Then, the amplitude of the wave is equal to

Options

A. `(lambda)/(4pi)`
B. `(2lambda)/(pi)`
C. `(lambda)/(2pi)`
D. `lambda`

Answer

A

Explanation

For a wave
`y = a sin "" (2pi)/(lambda) (vt -x)" "…(i)`
Differentiating Eq. (i) w.r.t. we get
`(dy)/(dt) = (2piva)/(lambda) cos ""(2pi)/(lambda) (vt-x)`
Now, maximum velocity is obtained when
` cos ""(2pi)/(lambda) (vt-x) = 1`
`therefore V_(max) = ((dy)/(dt))_(max) =(2piva)/(lambda)`
but `V_(max) = (V)/(2) " "`(given)
`therefore (v)/(2) = (2piva)/(lambda)`
`rArr = (lambda)/(4pi)`