Measuring the Speed of Sound in Air
Introduction: The velocity of all waves is given by the formula:
v=fx
where:
v is the speed of the wave measured in m/s,
f is the frequency of the wave measured in hertz, and
 is the wavelength of the wave measured in m.
Sound waves created by a tuning fork vibrating at 256 vibrations per second are said to have a frequency
of 256 hertz (vibrations per second). The frequency of a wave is not necessarily the same as the
frequency of the generating wave.
Resonance or sympathetic vibration may occur when an object is exposed to forced vibrations.
If the frequency of these “forced” vibrations matches the object’s “natural frequency” the object may
begin to vibrate or, if it is already vibrating, a dramatic increase in the amplitude of these vibrations may
occur. When either of these happens it is called resonance or sympathetic vibration. For example: A
person who sings next to a piano may cause the piano strings that produce similar frequencies to vibrate.
Resonance occurs when the natural vibration rates of two objects are the same or when the vibration rate
of one of them is equal to one of the harmonics of the other. Another example occurs when a singer
sings a note that matches the natural frequency of crystal (glass). As the note is continued with a large
amplitude (volume) the crystal will begin to resonate (vibrate) more and more violently until it breaks
apart.
Gases (air) can resonate as well: organ pipes, flutes and soda pop bottles make sound by resonating
air. A vibrating tuning fork held over an open tube may vibrate the air column in that tube at its
resonant or natural frequency. The length of the air column can be shortened or lengthened by adding or
draining water in the tube. The volume of the sound becomes loudest when the proper length for
maximum resonance at that frequency of the tuning fork occurs. For a tube open at one end and blocked
at the other, resonance first occurs when the air column is one fourth the wavelength of the sound wave
generated by the tuning fork.
In this experiment you will use the concept of resonance to determine the wavelength of a sound
wave of known frequency. You can then compute the speed of sound by multiplying the frequency by
the wavelength.
LAB # 15-1
Velocity of Sound in Air
MATERIALS: Resonance tube set up, tuning forks of 256 Hz or more, calculator
PURPOSE: Write your own after reading the lab.
HYPOTHESIS: What is the speed of sound in air in m/s?
PROCEDURE: (Groups may want to spread out)
1. Measure and record the inside diameter of the resonance tube and convert to meters. Record this in
row 1 of the data table.
2. Multiply this diameter by 0.4 and enter this value in row 2 in the data table.
3. Select and record the frequency of a tuning fork and enter this frequency in row 6 of the data table
4. Add water to the container until the resonance tube is about ¾ full. Slowly move the container and
see how it affects the water in the resonance tube. Practice moving the container and try to gain a
feel of the water movement. This movement will create the closed end of your tube. By adjusting
the water level you will change the length of the column of air.
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5.
Strike the tuning fork on the heel of your hand. Hold the vibrating tuning fork horizontally as close
to the open end of the tube as you can. Move the container, varying the length of the air column.
Try to find the spot where the sound is best reinforced (loudest). You may find more than one
position where reinforcement occurs, so try moving the container up and down several times to find
the shortest tube length that gives the loudest sound.
6. Measure and record the length of the air column in row 3 of the data table - that is the distance from
the top of the tube to the top of the water.
7. Add the adjusted diameter value (row 2) to the measured column of air from step # 6 (row 3) and
enter it as the length of the air column (row 4). The reason for doing this is that the column must
be increased by four tenths (0.4) of the diameter of the tube to correct for the small amount of air
just outside the top of the tube that vibrates with the air column in the tube.
8. Compute the wavelength of that sound by multiplying the corrected length value you made in step
#7 (row 4) by 4. The corrected length is only one fourth of the wavelength of the sound vibrating
in the air column. Record this wavelength in row 5 of your data table.
9. Using the frequency and the wavelength you calculated, calculate the velocity of that sound and
record in row 7. Velocity of a wave is found by the formula v = f x .
10. If time permits, repeat the steps above using a different tuning fork.
11. Answer question #1 below to get the accepted value for the speed of sound and calculate your %
error for each trial and enter in row 8 of your data table. For % errors > 5% re-measure.
DATA TABLE:
Row
1
2
3
4
5
6
7
8
Data Entry
Trial 1
Trial 2
Diameter of the tube in meters
0.4 x the diameter of the tubes in meters
Length of the air column in meters
Corrected length of the air column (row 2 + row 3)
Wavelength in meters (row 4 x 4)
Frequency of the tuning fork in Hertz
Velocity of sound in air in m/s
% error (answer question #1 to calculate accepted value)
QUESTIONS:
1.
The room temperature at the time of the lab was _______ºC. The velocity of sound in air is 332
m/s at 0º Celsius. It increases 0.6 m/s for each Celsius degree above zero. Calculate the velocity of
sound at the temperature of the laboratory.
2.
How does your computed value for the velocity of sound compare with the accepted value?
3.
Sound waves travel in water about four times faster than in air. When sound waves leave air and
enter water, the equation v = f x  tells us that since velocity increases, either frequency (f) or
wavelength () or both must increase. From previous information you have obtained, does f, , or both
increase and why?
4.
An observer sees a lightning flash from a distant thunderstorm and 12 seconds later she hears the
thunder. If the temperature of the air is 20º C, how far from the storm is the observer? (Assume that
light travels instantaneously).
ANALYSIS & REFLECTION:
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