2-6 Resonance in air columns

Example 1

Organ pipe A, with both
ends open, has a fundamental frequency of 20 Hz. The third harmonic of organ
pipe B, with one end closed has the same frequency as the second harmonic of
pipe A. How long is pipe B?
Speed of sound in air v_{air}
= 343 m/s.

L_{B }=
m

Answer

Since organ pipe A is open at both ends, the resonant frequencies must satisfy the relationship

where v is the speed of sound in air and L_{A}
is the length of pipe A.
For the fundamental
frequency n = 1 and the frequency is

Organ pipe B is closed at one end. The resonant frequencies are given by

where v is the
speed of sound in air and L_{B} is the length of pipe B.

We know that