Casio EA-200, EA200 2n–1λ

Column of Air Resonance and

the Velocity of Sound

This activity uses the resonance of a column of air to measure the velocity of sound.

Theory

Resonance is what occurs when one object vibrating at the same natural frequency of a second object causes the second object to vibrate. If you have two tuning forks of the same natural frequency located near each other and strike one of the tuning forks so begins vibrating, the other tuning fork will also vibrate even if you do not strike it. This is due to resonance.

This activity uses a fixed-frequency sound source to produce resonance in a vertical resonance tube. The sound produced by the resonating column of air will sound louder than the sound produced by the sound source.

The expressions below show the relationships between the length of the column of air and wavelength, and the velocity of sound and wavelength. The relationship between the velocity of sound and wavelength is called the basic equation.

Ln =	2n–1 λ –	L v = f	λ
	4

Ln(m) : Air Column Length for Resonance Point n (n = 1, 2, 3...)

L(m) : Air Column Open-end Correction

λ(m) : Wavelength of Sound

v(m/s) : Velocity of Sound

f(Hz) : Frequency of Sound Wave

1Resonance Point 1

2Resonance Point 2

Actually, the air around the opening in the resonance tube also behaves like part of the air column. This is called “open-end correction.” The effects of open-end correction can be eliminated by measuring the length of the air column at Resonance Point 1 and Resonance Point 2 and calculating the difference between the two. This can be used in combination with the wave basic equation to determine the velocity of sound, using the expression below.