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

Answer

D

Explanation

Given y = a sin `2 pi ( bt - cx)`
Comparing it will general equation
`y = r sin [ (2 pi t)/(T) - (2pi)/(lambda) x]`
We got , `(2pi )/(T) - omega = 2 pi b`
and r = a
`implies lambda = (1)/(c) ` and ` T = (1)/(b)`
Maximum particle velocity
`omega r = 2 pi ba `
Wave velocity ` v = (lambda)/(T) = (b)/(c)`
Given maximum particle velocity = 2 `xx` wave velocity
`2 pi ba = 2 xx (b)/(c) implies c = (1)/(pi a )`