For the travelling harmonic wave `y ( x,t) = 2.0 cos 2pi``( 10t- 0.0080x+0.35)` where x and yare in cm and t in s. Calculate the phase differencebetween oscillatory motion of two points separated by a distance of
a) 4m, (b) 0.5m
(c ) `lambda //2` (d) `3lambda //4`

Explanation

The given equation be written as
`y =2.0 cos [ 2p( 10t-0.0080x) + 2pi xx0.35]`
`y =2.0 cos[ 2pi xx 0.0080 ((10t)/(0.0080) -x)+ 0.7 pi]`
Compare it with the standard equation of a travelling harmonic ,we have
`y =r . Cos[(2pi)/(lambda) (vt-x) + ph_(0)]`
We get, `(2pi)/( lambda)= 2pixx0.0080`
Further ,we know that
phase diff. `phi=( 2pi)/( lambda) x `
(a) Whe `x = 4m= 400 cm `
`phi =( 2pi)/(lambda).x =2pixx0.0080xx400`
`= 6.4 pi rad.`
(b) When`x =0.5=50 cm`
`phi= ( 2pi)/( lambda ) .x = 2pixx0.0080 xx50`
`= 0.8 pi ` rad.
(c ) When `x = ( lambda)/(2)`
`phi = ( 2pi)/( lambda) xx( lambda )/(2)= pi`rad.
(d) When `x= (3 lambda)/( 4)`
`phi = ( 2pi)/( lambda) xx ( 3 lambda)/( 4) = ( 3lambda)/(2)` rad.