A source of sound gives 4 beats per second when sounded with another source of frequency $250 \mathr

Question

A source of sound gives 4 beats per second when sounded with another source of frequency $250 \mathrm{~Hz}$. The second harmonic of the source, together with a source of frequency $516 \mathrm{~Hz}$ gives 8 beats per second. What is the fundamental frequency of the source?

Professor PC Thomas Classes · Answer

(a) : Let the fundamental frequency of the unknown source be $f$. From the first condition, $f$ gives 4 beats with $250 \mathrm{~Hz}$, so $f = 250 \pm 4$. Thus, $f = 254 \mathrm{~Hz}$ or $246 \mathrm{~Hz}$. The second harmonic is $2f$. From the second condition, $2f$ gives 8 beats with $516 \mathrm{~Hz}$, so $2f = 516 \pm 8$. Thus, $2f = 524 \mathrm{~Hz}$ or $508 \mathrm{~Hz}$, which implies $f = 262 \mathrm{~Hz}$ or $254 \mathrm{~Hz}$. The common value that satisfies both conditions is $f = 254 \mathrm{~Hz}$.