Column Of Air Resonance And The Velocity Of Sound - Casio EA-200 User Manual

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.
2n–1
λ f λ
L L v
=
=
–
n
4
L
(m) : Air Column Length for Resonance
n
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
1 Resonance Point 1
2 Resonance 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.
v
2-7-1
English
í Equipment
Glass Resonance Tube (Uniform Inside Diameter, With Scale Markings)
Rubber Tube Reservoir
Low Frequency Generator (or Tuning Fork)
Audio Measurement Setup (EA-200, graphic scientific calculator,
data communication cable)
Temperature Measurement Setup (EA-200, graphic scientific calculator,
data communication cable, temperature probe)
í Setting Up
u Set up the equipment as shown in the illustration, and fill with water, taking care it does
not overflow.
u Raise and lower the reservoir and check to make sure that the level of the water changes.
Glass Resonance Tube
1
2 Tube Length: 1 meter
Stand
3
4 Reservoir
5 Rubber Tube
6 Low Frequency Generator:
800Hz
Speaker
7
8 EA-200
20020601
Activity: Setup Activity: Setup
Stand