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Question

The number of possible modes of natural oscillations of air column in a pipe closed at one end of length 170 cm below frequency 1450 Hz are
[velocity of sound =340 ms1]
  1. 14
  2. 13
  3. 12
  4. 15


Solution

The correct option is A 14
Fundamental frequency for closed organ pipe,
f0=v4L
f0=3404×1.70=50 Hz
Natural frequencies can exist as odd multiple of f0.
So, natural frequencies are,
f0,3f0,5f0......
50 Hz, 150 Hz, 250 Hz,.......
For this arithmetic progression, let us suppose nth term is 1450 Hz.
So, tn=a+(n1)d
1450=50+(n1)100
n=15
So, total 14 modes are possible.

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