Question

Find the fundamental and the first overtone of a 15 cm pipe 

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

(b) If the pipe is open at both ends,

(c) How many overtones may be heard by a person of normal hearing 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 i^th over tone is given by n₁ = (i + 1) x n₀ where i = 1,2,3 ...etc. frequency of the fundamental 

(a) n₀ = v/4L where n₀ = frequency of the

fundamental  =  n₀ = 330/4 x 0.15 = 550Hz

(b) The first four overtones are 2n₀ , 3n₀ , 4n₀ ,and 5 n₀. So, the required frequencies are 1100, 2200, 3300, 4400, and 5500 Hz.

(c) the frequency of the nth overtone is (2n + 1)r

(2n + 1)n₀ = 20000; or (2n + 1) 550 = 20000

or n = 17.68

Or n = 17.18 the acceptable value is 17.