For the travelling harmonic wave, `y(x,t)=2.0cos2pi[10t-0.0080x+0.35]`. Where x and y are in cm and t is s, what is the phase difference between oscillatory motino at two points separated by a distance of (i) 4m (ii) 0.5m (iii) ` lambda//2` (iv) `3lambda//4` ?

Explanation

The given equation can be rewritten as
`y=2.0cos[2pi(10t-0.0080x)+2pixx0.35]`
`y=2.0cos[2pixx0.0080((10t)/(0.0080)-x)+0.7pi]`
Compare it with the standard equation of a travelling harmonic wave, `y=rcos [(2pi)/(lambda)(upsilont-x)+phi_(0)]`
we get, `(2pi)/(lambda)=2pixx0.0080`
Further, we know that for the path difference x, the phase diff., `phi=(2pi)/(lambda)x`
(i) when, `x=4m=400cm`
`phi=(2pi)/(lambda)x=2pixx0.0080xx400=6.4pirad`
(ii) when, `x=0.5=50cm`
`phi=(2pi)/(lambda)x=2pixx0.0080xx50=0.8pirad`
(iii) when, `x=lambda//2`
`phi=(2pi)/(lambda)xx(lambda)/(2)=pirad`
(iv) when, `x=3lambda//4`
`phi=(2pi)/(lambda)xx(3lambda)/(4)=(3pi)/(2)rad`