Question

Determine the fundamental frequency and the first four overtones of a 15 cm pipe

(a) If the pipe is closed at one ends,

(b) If the pipe is open at both ends

(c) How many overtones are within the human auditory range in each of the above cases? Velocity of sound in air = 330 ms-1

Answer 1

For the organ pipe closed at one end, the fundamental frequency of the wave of wavelength λ is given by n0 = v/4L The frequency of ith over tone is given by ni=(i+1) x n0 where i=1,2,3…. etc.

(a) n0 = V/4I

Wher n0 = frequency of the fundamental node

The first four overtones are 3n0 , 5n0 , 7n0 and 9n0

∴ So, the required frequencies are 550, 1650, 2750, 3850, and 4950 Hz.

The first overtones are 2n0, 3n0 , 4n0 and 5n0

So, the required frequency are 1100, 2200, 3300, 4400, and 5500 Hz

The frequency of the nth overtone is (n +1) n0 .

∴ (n +1) n0 =20000 or (n+1)100 = 20000

Or n = 17.18

The acceptable value is 17.