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 m s-1)

Fundamental frequency of the closed organ pipe is

$v = \frac{v}{4 L}$

$Here, v = 340 m s^{- 1}, L = 85 cm = 0.85 m$

$∴ v = \frac{340 m s^{- 1}}{4 \times 0.85 m} = 100 Hz$

The natural frequencies of the closed organ pipe will be

$v_{n} = (2 n - 1) v = v, 3 v, 5 v, 7 v, 9 v, 11 v, 13 v, \dots$

$= 100 Hz, 300 Hz, 500 Hz, 700 Hz, 900 Hz$

$1100 Hz, 1300 Hz, \dots and so on.$

Thus, the natural frequencies lies below the 1250 Hz is 6.

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 m $s^{- 1}$ )