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]
  1. (a) 3
  2. (b) 2
  3. (c) 1
  4. (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 $n = \frac{2 \times 1000 \times 16.6 \times 10^{-2}}{332} = 1$

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