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A tuning fork of frequency 256 Hz produces 5 beats per second with a vibrating piano string. When the tension in the piano string is increased slightly, the beat frequency falls to 2 beats per second. What was the frequency of the piano string before the tension was increased?

1. (256+2) Hz
2. (256−2) Hz
3. (256−5) Hz
4. (256+5) Hz

Correct answer: (256−5) Hz

Solution

The initial beat frequency of 5 Hz indicates that the piano string's frequency was 5 Hz lower than the tuning fork's frequency of 256 Hz, making it 251 Hz. When the tension is increased, the frequency of the string rises, resulting in a new beat frequency of 2 Hz, confirming that the original frequency was indeed 251 Hz.

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