Question 33: Waves

Question

A source of sound gives 5 beats per second, when sounded with another source of frequency 100 s$$^{-1}$$. The second harmonic of the source, together with a source of frequency 205 s$$^{-1}$$ gives 5 beats per second. What is frequency of the source?

Accepted Answer

Let the frequency of the sound is $$f$$.
In first case,
$$\begin{aligned}
f & =100 \pm 5 \
& =105 \mathrm{~Hz} 	ext { or } 95 \mathrm{~Hz}
\end{aligned}$$
The frequency of second harmonic $$=2 f$$
According to second case,
$$\begin{aligned}
2 f & =200 \pm 10 \
& =210 \mathrm{~Hz} 	ext { or } 190 \mathrm{~Hz}\end{aligned}$$
If 5 beats are produced with frequency $$105 \mathrm{~Hz}$$, then frequency of second harmonic will be $$210 \mathrm{~Hz}$$.
i.e.
$$\begin{array}{r}
2 f=210 \
\Rightarrow f=105 \mathrm{~Hz} \
=105 \mathrm{~s}^{-1}
\end{array}$$

Answer

95 s$$^{-1}$$

Answer

105 s$$^{-1}$$

Answer

100 s$$^{-1}$$

Answer

205 s$$^{-1}$$

Waves

A source of sound gives 5 beats per second, when sounded with another source of frequency 100 s$^{-1}. The second harmonic of the source, together with a source of frequency 205 s^{-1}$ gives 5 beats per second. What is frequency of the source?

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