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

• A. 205 Hz
• B. 195 Hz
• C. 200 Hz
• D. 210 Hz

Answer 1

Answer: (A)

First case: Frequency $=v$;
No. of beats $/ sec$. $=5$ and
frequency (sounded with) $=200 \,Hz$.
Second case: Frequency $=2$ v; No. of beats $/ \sec =10$
and frequency (sounded with) $=420 \,Hz$.
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 $205 \,Hz$.