Champlain College
Physics 203-NYC
Resonance of an Air Column
Abstract
The objective of this lab is to study longitudinal standing waves in an air column
open at one end, and to measure the speed of sound in air.
1
Material
• Variable length air column
• Three tuning forks (1024 Hz, 512 Hz, and 384 Hz)
• Thermometer
2
Theory
The speed of sound in air can be obtained using the following equation:
s
v = (331.5 m/s) 1 +
Tc
273.15
(1)
where Tc is the measured temperature in celsius.
When a tuning fork of known frequency is allowed to vibrate, it produces a traveling
sound wave of fixed wavelength determined by the relationship
v = λf
(2)
When this wave enters an air column opened at one end and closed at the other, it can set up
a standing wave if the correct boundary conditions for this standing wave to exist are met,
as shown in figure 1. The sound heard, when the air column resonates with the standing
wave, will have its intensity amplified. As the length of the air column is increased, a longer
standing wave, of the same wavelength can be set up in the tube as shown in figure 1. The
distance between two successive resonance is therefore λ/2.
You will use this to calculate the speed of sound in air, and compare to the speed of
sound obtained using equation (1).
3
Procedure
1. Record the air temperature (in ◦C) at the position you are working. Make sure that
the mercury bulb is not touching anything except the air.
2. Slide the metal reservoir to the top of the stand. Add water to the air column until
the water level is 3 to 4 cm from the top.
Rémi Poirier
page 1 of 3
Champlain College
Physics 203-NYC
Figure 1: As the air column increase in length, more of the same standing wave can fit inside the
tube.
3. Make the 1024 Hz fork vibrate loudly and hold it above the air column such that the
ends of the fork are vibrating up and down. DO NOT HIT THE TUNING FORK
WHILE IT IS CLOSE TO THE GLASS TUBE, it may break the glass if the
fork hits the side of the tube.
4. While the fork is vibrating, lower the water, by lowering the can, until the first
resonance point is found. Repeat until you have reached the lowest position the water
can be in the tube. Make sure the water does not overflow. Record the water
level of each resonance to the nearest 1 mm. This is tedious and time consuming, and
can only be achieved with team work.
5. Calculate the wavelength λ from your measurements. To do so, you will need to make
four estimates of λ/2 from five resonance points. This is done by subtracting the
positions of two adjacent resonance points. Find the average of these four estimates
and calculate λ from this average.
6. Using the nominal value for the frequency of 1024 Hz fork, calculate the speed of sound.
v = λf .
Rémi Poirier
page 2 of 3
Champlain College
Physics 203-NYC
7. Repeat steps 2 to 6 for the two other forks. Note that you will have fewer successive
resonance points if the wavelength is longer.
8. Record the temperature again to make sure it did not change. If so, this will increase
the uncertainties on the calculated speed of sound.
9. Calculate the average of the three speeds obtained above
10. Compare this average to the value obtained from equation (1).
4
Analysis
1. On a single page, write a summary of your data, analysis and conclusion.
Rémi Poirier
page 3 of 3