Question

A long pipe organ is 10 m tall. It has an open end and closed end. Find

the fifth harmonic frequency of this pipe organ pipe when the speed of
sound in the organ is 340 m/s.

Answer 1

Resonances occur at:

OC OCOC OCOCOC OCOCOCOC OCOCOCOCOCλ

λ/4 3λ/4 5λ/4 7λ/4 9λ/4

A resonance occrurs at λ/4

Thereafter, resonance occurs every λ/2

The fifth resonance will occur at λ/4 + 2λ = 9λ/4

If λ / 4 = 10 m then λ = 40 m

9 λ / 4 = 10 m because the pipe is 10 m long

λ = 40 m / 9 = 4.44 m the fifth resonance occcurs at a wavelength of 4.44 m

f λ = c = 340 m/sec

f = 340 m/sec / 4.44 m = 76.5 / sec

Note: the first resonance occurs at f = 340 / 40 = 8.5 /sec