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Periodic Motion

A guitar stri...

Question

A guitar string produces $4$ beats/s when sounded with a $350 H z$ tuning fork and $9$ beats/s when sounded with a $355 H z$ tuning fork. What is he vibrational frequency of the string? Explain your reasoning.

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Solution

At 350 Hz, and 4 beats/s, the other string could be 354 or 346 Hz, and at 355 Hz, and 9 beats/s, the other string could be 346 Hz, or 364 Hz.

Based on the information given in question, the frequency is 346 Hz since it works in both scenarios.

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