For a travelling harmonic wave `y=2.0 cos(10t-0.0080x+0.35)`, where x and y are in centimetres and t in seconds. What is the phase difference between oscillatory motion of two points separated by a distance of (a) 4m (b) 0.5 m (c ) `lambda//2` (d) `3lambda//4`

Explanation

Equation for a travelling harmonic wave is given as:
`y (x, t) = 2.0 "cos "2pi (10t – 0.0080x + 0.35)`
`y (x, t) = 2.0 "cos" 2pi (10t – 0.0080x + 0.35)`
Where,
Propagation constant, k `= 0.0160 pi`
Amplitude, a = 2 cm
Angular frequency, `omega= 20 pi` rad/s
Phase difference is given by the relation:
`phi=kx=(2pi)/(lambda)`
(a) For x = 4 m = 400 cm
`phi = 0.016 pi × 400 = 6.4 pi` rad
(b) For 0.5 m = 50 cm
`phi = 0.016 pi xx 50 = 0.8 pi` rad
(c) For `x=(pi)/(2)`
`phi=(2pi)/(lambda)xx(lambda)/(2)=pi` rad
(d) For `x=(3lambda)/(4)`

`phi=(2pi)/(lambda)xx(3lambda)/(4)=1.5 pi` rad