Question

An open organ pipe is 1.8m long. If the speed of sound is 343m/s, what are the pipes:           a) fundamental , b) 1st overtone , & c) 2nd overtone ?

Answer 1

In an open tube antinodes are located at the ends of open tube. Minimum number of waves that can fit in an open tube with minimum number of nodes and antinodes is λ/2. Next higher number of wavelengths would be λ, 3/2λ, 2λ.......
a) Fundamental means first harmonic

λ/2 = length

λ = 2 * 1.8 = 3.6 m

frequency = wave speed/wavelength

frequency = 343/3.6

frequency = 95.27 Hz

b) 1st overtune

λ = length

λ = 1.8 m

frequency = 343/1.8 = 190.55 Hz

c) 2nd overtone

3λ/2 = length

3λ = 1.8 * 2

λ = 1.2 m

frequency = 343/1.2

frequency = 285.83 Hz