Q145 / 180 · COMEDK 2020 · Physics
A source of sound gives 5 beats per second, when sounded with another source of frequency $100 \mathrm{~s}^{-1}$. The second harmonic of the source, together with a source of frequency $205 \mathrm{~s}^{-1}$ gives 5 beats per second. What is frequency of the source?
- A$95 \mathrm{~s}^{-1}$
- Correct answerB$105 \mathrm{~s}^{-1}$
- C$100 \mathrm{~s}^{1}$
- D$205 \mathrm{~s}^{-1}$
Solution
Let the frequency of the sound is $f$.
In first case, $f=100 \pm 5$
$$
=105 \mathrm{~Hz} \text { or } 95 \mathrm{~Hz}
$$
The frequency of second harmonic $=2 f$
According to second case.
$$
\begin{aligned}
2 f &=200 \pm 10 \\
&=210 \mathrm{~Hz} \text { or } 190 \mathrm{~Hz}
\end{aligned}
$$
If 5 beats are produced with frequency $105 \mathrm{~Hz}$, then frequency of second harmonic will be $210 \mathrm{~Hz}$.
i.e.
$2 f=210$
$\Rightarrow \quad f=105 \mathrm{~Hz}$
$=105 \mathrm{~s}^{-1}$
Hence, the correct answer is option: 'B'.