12.9.4 – Stationary Waves in Closed Pipes*

(ADVANCED PHYSICS TOPIC)

Blowing across the top of a pipe or bottle will produce a sound. This is caused by standing waves in the pipe.

In general we can see that the frequency for the nth harmonic is given by:

But only exists for odd values of n.

 

A clarinet is a musical instrument that behaves like a closed pipe.

 

Example
A note of constant frequency is produced by a loudspeaker placed above an open pipe with a movable piston. The length l of the air column is slowly increased from zero. When l reaches 17.0 cm, the sound detected increases greatly in volume.

Calculate
(a) the wavelength of the note produced by the loudspeaker, and

First harmonic: λ / 4 = 17.0

λ = 68.0 cm

 

(b) the next length l when the sound detected increases greatly in volume.

No change in frequency, velocity or wavelength

Third harmonic: l = 0.75 λ
= 0.75 (68.0)
= 51.0 cm

 

 

 

2025 Physics Lessons