When a wave travels in a medium, the particle displacement is given by the equation `y= a sin 2 pi (bt-cx)` where a, b and c are constants. The maximum particle velocity will be twice the wave velocity, if

Options

A. `c=1/(pi a)`
B. `c= pi a`
C. `b=ac`
D. `b=1/(ac)`

Answer

A

Explanation

The maximum particle velocity is twice the wave velocity
`a omega =2 (omega/k)`
or ak=2….(i)
Given `y=a sin 2 pi (bt-cx)`
or `y=a sin (2 pi bt-2 pi c x)`
The general wave equation
`y=a sin (omega t-kx)`
then k=`2 pi c`
`therefore a 2 pi c=2`[ From Eq. (i)]
or `c=1/(pi a)`