Question

A simple harmonic progressive wave is represented as `y = 0.03 sin pi(2t - 0.01x)` m. At a given instant of time, the phase difference between two particles 25 m apart is
A. `pi` rad
B. `(pi)/(2) rad`
C. `(pi)/(4)` rad
D. `(pi)/(8)` rad

Answer 1

Correct Answer - C
The given equation of SHM wave in
`y = 0.03 sin pi (2t - 0.01)xx m`
` = 0.03 sin (2pi t - 0.01pi x)m`
Comparing it with general equation , we get
`y = a sin (omega t - kx)`
where , `" "k = (2pi)/(lambda) rArr lambda = 200 m`
The phase difference between two particle is given by `Delta phi = k x = (2pi)/(lambda) xx x " ".....(i)`
Here, `x = 25m`
Substitunting the value of x and `lambda` in Eq (i) , we get `Delta phi = (2pi)/(200) xx 25 =(pi)/(4) rad`.