Question

The path difference between the two waves :

y₁ = a₁ sin (wt – kx) and y₂ = a₂ cos (wt – kx + f) is –

• A. (l/2p)f
• B. $\lambda\left( \frac{\varphi + (\pi/2)}{2\pi} \right)$
• C. $\frac{2\pi}{\lambda}\left( \varphi –\frac{\pi}{2} \right)$
• D. $\left( \frac{2\pi}{\lambda} \right)\varphi$

Answer 1

Answer: (B)

$\lambda\left( \frac{\varphi + (\pi/2)}{2\pi} \right)$

Answer 2

Relation between phase difference and path difference

D f =

y₁ = a₁ sin (wt – kx)

y₂ = a₂ cos (wt – kx + f)

From phasor diagram : -

Dx = $\frac { \Delta \phi } { 2 \pi }$ × l

= $\frac { 1 } { 2 \pi }$ $\left( \frac { \pi } { 2 } + \phi \right) \lambda$