The path difference between the two waves :

$y_{1} = a_{1} \sin (ω t - \frac{2 πx}{λ})$ and
$y_{2} = a_{2} \cos (ω t - \frac{2 πx}{λ} + ϕ)$ is

Question

The path difference between the two waves : y 1 = a 1 sin ⁡ ω t - 2 πx λ and y 2 = a 2 cos ⁡ ω t - 2 πx λ + ϕ is

TestHub · Accepted Answer

Relation between phase difference and path difference.

$Δ ϕ = \frac{2 π}{λ} Δ x$

$y_{1} = a_{1} \sin (ω t - k x)$

$y_{2} = a_{2} \cos (ω t - k x + ϕ)$

$y_{2} = a_{2} \sin (ωt - kx + ϕ + \frac{π}{2})$

$Δ x = \frac{Δ ϕ}{2 π} \times λ$

$= \frac{1}{2 π} (\frac{π}{2} + ϕ) λ$

Physics - Sound Wave Question with Solution | TestHub

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