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The number of possible natural oscillations of air column in a pipe closed at one end of length 85 cm whose frequencies lie below 1250 Hz are: (velocity of sound = 340 $ms^{-1}$)
A
4
B
5
C
7
D
6
Detailed Solution
For a closed organ pipe, $f_n = (2n + 1)\frac{v}{4l}$, with $\frac{v}{4l} = \frac{340}{4\times0.85} = 100$ Hz
$f_0 = 100$ Hz, $f_1 = 300$ Hz, $f_2 = 500$ Hz, $f_3 = 700$ Hz, $f_4 = 900$ Hz, $f_5 = 1100$ Hz
These six frequencies are below 1250 Hz.
$f_0 = 100$ Hz, $f_1 = 300$ Hz, $f_2 = 500$ Hz, $f_3 = 700$ Hz, $f_4 = 900$ Hz, $f_5 = 1100$ Hz
These six frequencies are below 1250 Hz.