When a wave travels in a medium, th eparticle 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

Particle displacment in harmonic wave is
`y=asin 2pi(bt-cx)`
particle velocity `V=(dy)/(dt)`
`=axx2pibcos2pi(bt-cx)`
Max. particle velocity `upsilon_(max)=axx2pib`
Comparing the equation of harmonic with the standard equation of harmonic wave
`y=rsin((2pi)/(lambda))(upsilont-x)=rsin2pi((upsilon)/(lambda)t-(x)/(lambda))`
we have, `(upsilon)/(lambda)=b` and `(1)/(lambda)=c` or `lambda=(1)/(c)`
`upsilon=blambda=(b)/(c)`
Given, `upsilon_(max)=2upsilon` or `axx2pib=2xx(b)/(c)` or `c=(1)/(pia)`