Principle of Superposition, Interference and Beats: Practice Problem & Solution
Two sources of sound placed close to each other are emitting progressive waves given by $y_1 = 4 \sin 600 \pi t$ and $y_2 = 5 \sin 608 \pi t$. An observer located near these two sources of sound will hear: (2012 Pre)
Solution Explained:
To solve this problem, we apply the core principles of Principle of Superposition, Interference and Beats. Understanding the underlying formula is key to arriving at the correct answer below:
From the equations, $\omega_1 = 600\pi \implies f_1 = 300 \text{ Hz}$, and $\omega_2 = 608\pi \implies f_2 = 304 \text{ Hz}$. Beat frequency = $304 - 300 = 4 \text{ Hz}$. Intensity ratio $I_{max}/I_{min} = (A_1 + A_2)^2 / (A_1 - A_2)^2 = (5+4)^2 / (5-4)^2 = 81:1$.
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