Experiment 12: Speed of Sound in Air
Figure 12.1: Sound Tube
EQUIPMENT
Sound Tube
(3) Tuning Forks (f
Mallet
Water Jug
Rubber Hose
Clamps and Rod
Paper Towels
300 Hz)
Figure 12.2: Displacement of Air
61
Experiment 12: Speed of Sound in Air
62
Advance Reading
Text: Speed of sound, longitudinal waves, wavelength,
frequency, standing wave, resonance.
Objective
The objective of this experiment is to measure the
speed of sound in air.
Theory
There are a variety of wave types.
Sound is a longitudinal wave requiring a medium in
which to propagate. A longitudinal wave is one in
which objects oscillate in the same direction the wave
propagates. The speed of sound depends on properties of the medium such as bulk modulus, density, and
temperature. The speed of sound is not a constant
value!
To calculate today’s speed of sound, v, we will determine the wavelength,
(lambda), of the sound produced by a tuning fork of known frequency, f :
v= f
(12.1)
A vibrating tuning fork generates a sound wave that
travels outward in all directions. When held above a
sound tube, a portion of the wave will travel down the
tube, reflect o↵ the water’s surface, then return to the
top. If the rising pressure wave reaches the top of the
tube as the next wave is produced, the wave is reinforced, and the sound will resonate. A standing wave is
generated in the tube, and the sound will be distinctly
louder. This occurs when the column of air in the tube
has an appropriate length (height) for a given tuning
fork.
When considering the displacement of air for resonance
(constructive interference), notice that there is an antinode near the open end of the tube, and a node at the
water’s surface from which the sound is reflected (refer to Fig. 12.2). To locate multiple resonances for a
particular tuning fork, one must be able to change the
length of the air column in the tube. This will be accomplished by adjusting the water level in the tube:
raise or lower the water reservoir, and the water level
in the tube will change accordingly.
The distance between one resonance and the next is
1
2 . This experiment will attempt to locate at least
three resonances to reduce uncertainty of the results.
2
= |x1
x2 |
(12.2)
Having calculated and being given f of a tuning fork,
the speed of sound can be calculated with Eq. 12.1.
Prelab 12: Speed of Sound in Air
63
Name:
1. What is a standing wave? (20 pts)
2. What is a resonant frequency? (20 pts)
3. Explain the relationship v = f . (20 pts)
4. Refer to Eq. 12.1 and Eq. 12.3 (Step 10 of the procedure). You measure
lab is 22 C. What is the frequency of this resonance? (40 pts)
1
2
to be 40 cm. The temperature in the
Experiment 12: Speed of Sound in Air
64
PROCEDURE
QUESTIONS
1. Raise the bottle of water until the tube is filled.
2. Hold a vibrating tuning fork above the tube and
lower the water level gradually until the sound becomes loudest (resonates). Raise the water level as
necessary.
3. Mark the water level with a rubber band.
4. Continue to lower the water level until all resonant
positions have been marked in this manner. Record
the positions in the data table provided.
1. Define ultrasonic, supersonic, and infrasonic.
2. As noted in the theory section, our sound tubes do
not have an anti-node at the open end of the tube.
Analyze your data and determine where, relative to
the open end of the tube, the anti-node is located
for each frequency used. State your answer in terms
of . Refer to Fig. 12.
5. Calculate the average distance “l” between resonance positions. Record it in the table provided.
3. Assume you are in a particular location (e.g., at the
beach, in the mountains, in the lab). Two sounds,
one a high frequency, one a low frequency, are generated. Does a high frequency sound travel faster
than a low frequency sound in a particular location?
6. Calculate the fundamental wavelength
record it.
4. Does sound travel at the same speed in di↵erent
materials? Specify the speed of sound in 3 media.
= 2l and
7. Calculate the measured speed of sound ve = f and
record it.
8. Repeat this process for two other frequencies (3 tuning forks, total).
9. Average your three values of v. Record them in the
data table on the board.
10. Calculate a theoretical value for the speed of sound,
vT , using:
vT = (331.5 + 0.6T )m/s
(12.3)
where T is the temperature in degrees Celsius.
11. Calculate your percent error. [Eq. A.1, Page 147]
Figure 12.3: Proper position for tuning fork
1
4
= d1 + d2
1
4
= distance from position of water’s surface
when 1st resonance is heard to anti-node.
d1 : Refer to Step 2.
d2 ⌘ distance from the top of the tube to the
anti-node.
Figure 12.4: Determination of anti-node location.