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=pia`
B. `c=1/(2pia)`
C. `c=1/(pia)`
D. `c=2pia`

Answer

C

Explanation

Given, wave equation,`y=asin2pi(bt-cx)`
Compairing the above equation with the general equation of the progressive wave which is given as,
`y=A_(0)sin2pi(ft-x/(lamda))`
we get, frequency, f = b, wavelength, `lamda= 1/c` and amplitude of the wave, `A_(0)=a`
As, we know, that the maximum velocity of the particle,
`V_(max)=A_(0)omega=axx2pib` ...(i)
Wave velocity, `v_(wave)=flamda`
`rArrv_(wave)=b/c` ...(ii)
It is given that,
`v_(max)=2v_(wave)`
So, by substituting the values from Eqs. (i) and (ii) in the above relation, we get
`a2pib=2b/c`
`thereforec=1/(api)`