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A source of sound gives 5 beats per second, when sounded with another source of frequency 100/sec. The second harmonic of the source, together with a source of frequency 205/sec gives 5 beats per second. What is the frequency of the source?

1. 95 sec⁻¹
2. 100 sec⁻¹
3. 105 sec⁻¹
4. 205 sec⁻¹

Correct answer: 105 sec⁻¹

Solution

The first condition gives two possible frequencies for the source: 95 Hz or 105 Hz (since beat frequency = |f₁ - f₂|). The second condition involves the second harmonic of the source, which is 2f. For 2f to give 5 beats with 205 Hz, |2f - 205| = 5. Solving this gives f = 105 Hz. Thus, the source frequency is 105 Hz.

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