An organ pipe open on both ends in the $n\text{th}$ harmonic is in resonance with a source of $1000\text{…
An organ pipe open on both ends in the $n\text{th}$ harmonic is in resonance with a source of $1000\text{ Hz}$. The length of pipe is $16.6\text{ cm}$ and speed of sound in air is $332\text{ m/s}$. Find the value of $n$. [JIPMER 2018]
(a) 3
(b) 2
(c) 1
(d) 4
Solution
Given, $f = 1000\text{ Hz}, v = 332\text{ m/s}$,
$l = 16.6\text{ cm} = 16.6 \times 10^{-2}\text{ m}$
Frequency in an organ pipe open on both ends,
$f = \frac{nv}{2l} \Rightarrow n = \frac{2fl}{v}$
or $n = \frac{2 \times 1000 \times 16.6 \times 10^{-2}}{332} = 1$