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A tuning fork of frequency 512 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

1. 510 Hz
2. 514 Hz
3. 516 Hz
4. 508 Hz

Correct answer: 510 Hz

Solution

The beat frequency is the difference between the tuning fork's frequency and the piano string's frequency. Initially, the beat frequency is 4 Hz, so the piano string's frequency could be either 512 + 4 = 516 Hz or 512 - 4 = 508 Hz. When the tension is increased, the frequency of the string increases, reducing the beat frequency to 2 Hz. This means the initial frequency must have been 510 Hz (512 - 2).

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