Principle of Superposition, Interference and Beats: Practice Problem & Solution
A tuning fork of frequency $512 \text{ Hz}$ makes 4 beats per second with the vibrating string of a piano. The beat frequency decreases to 2 beats per sec when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was: (2010 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:
Possible frequency of string is $512 \pm 4 = 508$ or $516 \text{ Hz}$. Increasing tension increases frequency. If it were $516$, new frequency would be $>516$, increasing beats $>4$. If it was $508$, new frequency could be $510$, decreasing beats to 2. Original was $508 \text{ Hz}$.
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