1.

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

Answer» Correct Answer - D
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 )`


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