Question

An organ pipe closed at one end has a fundamental frequency of $1500\text{Hz}$. The maximum number of overtones generated by this pipe which a normal person can hear is

• A. $14$
• B. $13$
• C. $6$
• D. $7$

Answer 1

The correct option is C $6$

Modes of vibration of air column in a closed organ pipe is given by

$f_n=\frac{(2n-1)v}{4L}\text{where}n=1,2,3,\mathrm{4.....}$

Fundamental frequency $f_0=\frac{v}{4L}=1500\text{Hz}$

Normal person can hear sound of frequency upto $20,000\text{Hz}$.

Therefore, $f_n=(2n-1)f_0=20,000$
$\Rightarrow 1500\times (2n-1)=20,000$
$\Rightarrow (2n-1)=13.33$
$i.e(2n-1)=13$ [odd harmonics]
$\Rightarrow n=7$

Total no. of modes of vibration that can be heard by the person is $7$.
$(6\text{overtones}+1\text{Fundamental frequency}$

Thus, option (c) is the correct answer.