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

Explanation

Comparing given wave equation
`y = 2 cos (20 t - 0016 x + 0.7 )cm`
with standard wave equation,
`y =a cos (omega t -kx + phi)`
we get, `k = 0.016 rad//cm`
Now, along the directon of propagation of wave, phase difference between two particles taking part in the propagation of wave, separated by distance x at any given instant is given by formula `del=kx.`
Here,
`(a) del = kx =0.016 xx 400 =6.4 rad`
(b)` del = kx = 0.016 xx 50 =0.8 rad`
(c) ` del = kx = (2pi )/(lamda) xx (lamda)/(2) =pi rad`
(d) `del = kx = (2pi)/(lamd a) xx (3 lamda )/(4) = (3pi)/(2)` rad