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When a wave travels in a medium, the par...

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

A

b=ac

B

`v=(1)/(ac)`

C

`c=pia`

D

`c=(1)/(pia)`

Text Solution

Verified by Experts

The correct Answer is:
D
(d) Given `y=a"sin"2pi(bt-cx)=a"sin"(2pibt-2pi cx)` Comparing it with general equation ,
`y=r"sin"[(2pit)/(T)-(2pi)/(lambda)x]`
We get, `(2pi)/(T)=omega=2pib` and r=a
Maximum particle velocity,
`omegar=2piba`
Wave velocity , `v=(lambda)/(T)=(b)/(a)`
Given, maximum particle velocity `=2 xx `wave velocity
`2piba=2xx(b)/(c)impliesc=(1)/(pia)`
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