Question

Two sources of in-phase coherent sound are located at the points (0 m, 2 m) and (-2 m, 0 m). An observer at the origin hears constructive interference because she is equidistant from both sources. However, if she moves in the +x direction, she hears destructive interference for the first time when she reaches the point (0.6 m, 0 m). What is the frequency of the sound that the sources are emitting? a) 476 Hz b) 391 Hz c) 335 Hz d) 295 Hz e) 244 Hz

Answer 1

c) 335 Hz

Step-by-step explanation:

Given that the two sources:

S₁ ≡ (0 m, 2 m)

S₂ ≡ (-2 m, 0 m)

The lady hears the destructive interference for the first time when she reaches the point (0.6 m, 0 m).

So, the path difference = Δx = |S₂P - S₁P|

`S_2P=\sqrt {(-2-0.6)^2+(0-0)^2}=2.6\ m`

`S_1P=\sqrt {(0-0.6)^2+(2-0)^2}=2.0881\ m`

So,

Δx = |2.6 - 2.0881| = 0.5119 m

For, first destructive interference, Δx = λ / 2

So,

Wavelength = 1.0238 m

Also,

c = ν×λ

Where,

c is the speed of sound wave having value as 346 m/s

ν is the frequency

λ is the wavelength

So,

ν = c / λ = 346 m/s / 1.0238 m ≈ 335 Hz