A source of frequency $f$ gives 3 beats/second when sounded with a source of frequency $300 \mathrm{

Question

A source of frequency $f$ gives 3 beats/second when sounded with a source of frequency $300 \mathrm{~Hz}$. The second harmonic (frequency $2f$) of the source gives 6 beats/second when sounded with a source of frequency $588 \mathrm{~Hz}$. The value of $f$ is

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(a) : From the first beat condition, the frequency $f$ of the source is $f = 300 \pm 3$, giving $f = 303 \mathrm{~Hz}$ or $297 \mathrm{~Hz}$. For the second harmonic $2f$, the beat frequency with $588 \mathrm{~Hz}$ is 6, so $2f = 588 \pm 6$. This gives $2f = 594 \mathrm{~Hz}$ or $582 \mathrm{~Hz}$. Dividing by 2 yields $f = 297 \mathrm{~Hz}$ or $291 \mathrm{~Hz}$. The overlapping frequency that satisfies both scenarios is $297 \mathrm{~Hz}$.