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Q.

An open pipe, when closed at one end, can resonate in its third harmonic with a frequency which is 100 Hz more than its fundamental frequency as an open pipe. If the fundamental frequency of the pipe when it is open at both ends is 50n Hz, then the value of n is

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a

8

b

4

c

2

d

0

answer is B.

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Detailed Solution

Length of the organ pipe is same in both the cases. Fundamental frequency of open pipe is $f_{1} = f_{2} be. f_{2} = 3 (\frac{v}{4 l})$
Given that $f_{2} = f_{1} + 100 Or f_{2} - f_{1} = 100$
Or $\frac{3}{4} (\frac{v}{l}) - (\frac{1}{2}) (\frac{v}{l}) = 100 \Rightarrow \frac{v}{4 l} = 100$

$∴ \frac{v}{2 l} or f_{1} = 200 Hz = 50 . nHz \Rightarrow n = 4$
$∴$ fundamental frequency of the open pipe is 200 Hz and n = 4

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