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

Options

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

Answer

A

Explanation

Eqation of the harmoic progressive wave give
`y=a sin 2pi(bt-cx)`
Here `2piv=omega=2omegab rArr v=b`
`K=(2pi)/(lambda)=2picrArr(1)/(lambda)=c`
(here c is the symbol givne for `(1)/(lambda)` and not the velocity)
`:.` Velocity of the wave `=vlambda=b(1)/(c)=(b)/(c)`
`(dy)/(dt)=a2pibcos2pi(bt-cx)=aomegacos(omegat-kx)`
Maximum particele velocity `=2omega=a2pib=2piab`
`i.e.,2pia=(2)/(c)or c=(1)/(pia)`