Let a disturbance y be propagated as a plane wave along the x-axis. The wave profile at the instants `t=t_(1) and t=t_(2)` are represent respectively as: `y_(1)=f(x_(1)-vt_(1)) and `y_(2)=f(x_(2)-vt_(2)). The wave is propagating withoute change of shape.

Options

A. the velocity of the wave is `v`
B. the velocity of the wave is `v=(x_(2)+x_(1)//(t_(2)+t_(1))`
C. the particle verlocity is `v_(p)=-vf(x-vt)`
D. the phase velocity of the wave is `v`

Answer

a., c., d.

Explanation

`y=f(x-vt)`
particle velocity.
`v_(p)=(dy)/(dt)=-vf'(x-vt)`
to find velocity of wave
`(d)/(dt)(x-vt)=0`
`(dx)/(dt)=v`