A source of frequency $v$ gives 5 beats/second when sounded with a source of frequency 200 Hz . The

Question

A source of frequency $v$ gives 5 beats/second when sounded with a source of frequency 200 Hz . The second harmonic of frequency $2 v$ of source gives 10 beats/second when sounded with a source of frequency 420 Hz . The value of $v$ is\

Professor PC Thomas Classes · Answer

(a) : First case: Frequency $=v$; No. of beats/second $=5$ and\ frequency (sounded with) $=200 \mathrm{~Hz}$\ Second case: Frequency $=2 \mathrm{v}$;\ No. of beats/sec and $=10$ and frequency (sounded with) $=420 \mathrm{~Hz}$\ In the first case, frequency $(v)=200 \pm 5=205$ or 195 Hz . And in the second case, frequency $(2 v)=420 \pm 10$\ or $v=210 \pm 5=205$ or 215 . So common value of $v$ in both the cases is 205 Hz .\