An organ pipe closed at one end has fundamental frequency of 1500 Hz . The maximum number of overtones generated by this pipe which a normal person can hear is (Normal man can hear the frequency up to

Question

An organ pipe closed at one end has fundamental frequency of 1500 Hz . The maximum number of overtones generated by this pipe which a normal person can hear is (Normal man can hear the frequency up to 19.5 kHz , Neglect end correction)

TestHub · Accepted Answer

The fundamental frequency of the closed pipe is $n = 1500$ Hz.

For an organ pipe closed at one end, only odd harmonics are present. The frequency of the $p$ -th overtone is given by:

$n_{p} = (2 p + 1) n$

The maximum frequency a normal person can hear is $19.5$ kHz $= 19500$ Hz. Thus, the frequency of the overtone must satisfy:

$(2 p + 1) n \leq 19500$

Substituting $n = 1500$ Hz:

$(2 p + 1) \times 1500 \leq 19500$

$2 p + 1 \leq \frac{19500}{1500}$

$2 p + 1 \leq 13$

$2 p \leq 12$

$p \leq 6$

The maximum number of overtones generated by this pipe which a normal person can hear is $6$ .

Answer: 6

Physics - Wave on String Question with Solution | TestHub

Options:

Doubts & Discussion