Principle of Superposition, Interference and Beats: Practice Problem & Solution
Two vibrating tuning forks produce progressive waves given by $y_1 = 4 \sin 500 \pi t$ and $y_2 = 2 \sin 506 \pi t$. Number of beats produced per minute is: (2005)
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:
Angular frequencies are $\omega_1 = 500 \pi$ and $\omega_2 = 506 \pi$, so $f_1 = 250 \text{ Hz}$ and $f_2 = 253 \text{ Hz}$. Beats per second = $253 - 250 = 3$. Beats per minute = $3 \times 60 = 180$.
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