Question

Wave of frequency 500 Hz has a phase velocity 360 ms^-1. The phase difference between two displacement at a certain point at time 10^-3 s apart will be ______.

Options

• (π) rad

• `(pi/2)` rad

• `(pi/4)` rad

• 2π rad

Answer 1

Wave of frequency 500 Hz has a phase velocity 360 ms^-1. The phase difference between two displacement at a certain point at time 10^-3 s apart will be (π) rad.

Explanation:

According to the concept of simple harmonic wave,

y = asin `(2pi)/lambda`(vt - Φ)

Now, phase angle at point "x" for time "t₁​"

t₁ = `(2pi)/lambda`(vt - x)

now for time "t_2​"

t_2​ = `(2pi)/lambda`(vt - x)

phase difference, `(phi_1-phi_2)=(2pi)/lambda("vt"_2-"x")-(2pi)/lambda("vt"_1-"x")` 

= `(2pi)/lambda"v"("t"_2-"t"_1)`

= `(2pi"n"lambda)/lambda("t"_2-"t"_1)`

= 2πn(t_2​ - t_1​)

= 2π × 500 × 10^-3

= π radian