Question

A plane transverse wave is propagating in a direction making an angle of \( 30^{\circ} \) with positive \( x \)-axis in the \( x \)-y plane. Find phase difference between points \( (0,0,0) \) and \( (1,1,1) \). Wavelength of the wave is \( 1 m \) :- 

(A) \( 2 \pi rad \) 

(B) \( (\sqrt{3}+1) \pi rad \) 

(C) \( (\sqrt{2}+1) \pi rad \) 

(D) None

Answer 1

OA = √2 cos 15° ⇒ △x

\(\because \) cos 15° = \(\frac{\sqrt3+1}{2\sqrt2}\)

Phase difference = \(\frac{2\pi}{\lambda}\) Path difference

△ϕ = \(\frac{2\pi}1\times\) △x

△ϕ = 2π x √2 cos15°

= 2π x √2 x \(\frac{\sqrt3+1}{2\sqrt2}\)

△ϕ = π (√3 + 1) rad

option (B)