The relation between particle velocity (v), the wave velocity (c) and the slope of the wave (s) is

Options

A. `v = -c s`
B. `c = - vs`
C. `v^(2) = - c^(2)s`
D. `c^(2) = - v^(2)s`

Answer

A

Explanation

The equation of the wave is
`y = A sin (omega t - kx)`
Differentiating w.r.t to 't'
`v = (dy)/(dt) = A omega cos (omega t- kx)`
Differentiating w.r.t. to 'x'
`s = (dy)/(dx) = - A k cos (omega t- kx)`
`(v)/(s) = (-omega)/(k) = - (2pi n)/((2pi//lamda)) = - n lamda = -c`
`:. v = - c s`