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

`y=asin2pi(bt-cx)`
`(v_(p))_(max)=aomega=a(2pib)`
`k=(2pi)/(lambda)=2pic` [where `c=(1)/(lambda)`]
`v=(omega)/(k)=(2pib)/(2pic)=(b)/(c)`
Given, `(v_(p))_(max)=2v`
`implies 2piab=2xx(b)/(c)impliesc=(1)/(pia)`.