Question

The path difference between two waves $y₁ = a₁ \sin\left(ω t - \frac2π xλ\right)$ and $y₂ = a₂ \cos\left(ω t - \frac2π xλ + φ\right)$ is

• A. $\frac\lambda2πφ$
• B. $\frac\lambda2π\left(φ + \frac\pi2\right)$
• C. $\frac2πλ\left(φ - \frac\pi2\right)$
• D. $\frac2πφλ}$

Hint:

$\cosθ = \sin(θ + π/2)$. Path difference = $(λ/2π) ×$ phase difference.

Answer 1

The Correct Option is B

Step 1: Convert $y₂$ to sine: $\cosθ = \sin\left(θ + \frac\pi2\right)$. So $y₂ = a₂ \sin\left(ω t - \frac2π xλ + φ + \frac\pi2\right)$.

Step 2: Phase difference = $φ + \frac\pi2$. Path difference = $\frac\lambda2π × phase difference = \frac\lambda2π\left(φ + \frac\pi2\right)$.