Question

Two waves are represented by the equations y₁ = a sin (ωt + kx + 0.87) m and y₂ = a cos (ωt + kx) m, where x is in metre and t in second. The phase difference between them is:

(a) 1.25 rad

(b) 1.57 rad

(c) 0.57 rad

(d) 1 rad

Answer 1

Correct option is : (d) 1 rad

y₁ = a sin (ωt + kx + 0.57)

and y₂ = a cos (ωt + kx)

or y₂ = a sin \((\frac{\pi}{2} + \omega t + kx)\)

As, ∆Φ = Φ₂ - Φ₁

\( = \frac{\pi}{2} - 0.57\)

\( = 1.57 - 0.57\)  

\( = 1 \ rad.\)