First slide

Superposition of waves

Question

Two waves are propagating to the point P along a straight line produced by two sources A and B of simple harmonic and of equal frequency. The amplitude of every wave at P is ‘a’ and the phase of A is ahead by $\frac{π}{3}$ than that of B and the distance AP is greater than BP by 50 cm. Then the resultant amplitude at the point P will be, if the wavelength is 1 meter

Moderate

A

2a
B

a $\sqrt{3}$
C

$a \sqrt{2}$
D

a

Solution

Path difference $(Δx) = 50 cm = \frac{1}{2} m$
$∴$ Phase difference $Δφ = \frac{2 π}{λ} \times Δx \Rightarrow φ = \frac{2 π}{1} \times \frac{1}{2} = π$
Total phase difference = $π - \frac{π}{3} = \frac{2 π}{3}$
$\Rightarrow A = \sqrt{a^{2} + a^{2} + 2 a^{2} \cos (2 π / 3)} = a$

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