Question

A simple harmonic progressive wave is represented as y = 0.03 sin π(2t - 0.01x) m. At a given instant of time, the phase difference between two particles 25 m apart is ______.

Options

• π rad

• `pi/2` rad

• `pi/4`rad

• `pi/8` rad

Answer 1

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

Explanation:

The given equation of SHM wave is

y = 0.03 sin π(2t - 0.01 x) m

= 0.03 sin (2πl - 0.01 πx)m

Compairing it with general equation, we get

y = a sin(ωt - kx)

where, k = `(2pi)/lambda`

`=> lambda` = 200 m

The phase difference between two particles is

given by `Delta phi = "kx" = (2pi)/lambda xx x`    ...(i)

Here, x = 25 cm

Substituting the values of x and λ in Eq. (i), we get

`Delta phi = (2pi)/200 xx 25 = pi/4` rad