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An organ pipe closed at one end has fundamental frequency of $1500 \mathrm{~Hz}$. The maximum number of overtones generated by this pipe which a normal person can hear is
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The correct answer is:
6
Human ear can hear frequencies upto $20,000 \mathrm{~Hz}$. So for closed pipe,
overtone, $\mathrm{v}=\frac{n v}{4 L}=n \times$ fundamental frequency
$$
\therefore \quad 20,000=n \times 1500 \Rightarrow n \approx 13 \text {. }
$$
Maximum possible harmonics obtained
$$
=1,3,5,7,9,11,13 \ldots \ldots \ldots \ldots
$$
Therefore one can hear maximum upto $13^{\text {th }}$ harmonics. Overtone $=7-1=6$
overtone, $\mathrm{v}=\frac{n v}{4 L}=n \times$ fundamental frequency
$$
\therefore \quad 20,000=n \times 1500 \Rightarrow n \approx 13 \text {. }
$$
Maximum possible harmonics obtained
$$
=1,3,5,7,9,11,13 \ldots \ldots \ldots \ldots
$$
Therefore one can hear maximum upto $13^{\text {th }}$ harmonics. Overtone $=7-1=6$
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