College Physics Lab
PH 144
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Standing Waves in an Air Column

Purpose:
To investigate the properties of standing sound waves in an air column which is open at one end and closed at the other. To determine the speed of sound in air.

Discussion:
The speed of sound waves v is related to the frequency f and wavelengthl by the usual formula v = f l. We also know that for a pipe filled with air, with one open end and one closed end, a standing wave is possible if there is a node at the closed end and an antinode at (or near) the open end. In this experiment, the 'closed end' corresponds to the surface of the water, and the 'open end' is always at the top of the pipe. The apparatus allows you to change the length of the air column by changing the water level. A tuning fork of known frequency f held near the open end will be used to send sound waves down the pipe. When the water level is at a standing wave node, the standing wave pattern is reinforced, and the sound intensity increases noticeably.

Procedure:

A. Explore resonance phenomena qualitatively:
Obtain 3 - 4 tuning forks of different frequency.
Make sure the flexible plastic tube is clamped shut. Make sure there is a tub beneath the large plastic tube to catch water spills. Fill the large tube with water nearly to the top.
Strike a low-frequency tuning fork on a rubber object, such as a large rubber stopper, and hold the end of the vibrating fork over the opening of the tube.
Lower the water level in the large tube by releasing the clamp on the flexible tube and allowing water to flow into a container.
How many resonances can you find? Do they all sound the same? About how far apart do they occur?
Repeat these steps for each of the higher-frequency tuning forks in succession.

B. Determine the speed of sound in air under current conditions:
Recall vair = fl
1. Determine the resonant wavelength.
• Determine the position of the water level for successive resonances using one tuning fork.
Find all of the possible resonance positions for that tuning fork.
• Using node-antinode diagrams determine the relationship between the resonant wavelength and the position for successive resonances.
• Determine a "best" value for the resonant wavelength from your data.

2. Calculate vair from f and l.

3. Using the temperature in the lab determine the appropriate value for vair using a formula or by looking up the value in the CRC handbook.

4. Compare your results with the known value. Express the comparison as a % difference.

5. Repeat steps 1 - 4 with a tuning fork having a different frequency.

C. Application: [If you finish steps 1-5, work on this.]
The human ear is approximately 2.7 cm long. The canal can be regarded as a tube open at one end and closed at the other. What are the frequencies of the 4 harmonics having the lowest frequencies?
The ear is most sensitive at a frequency of about 3000 Hz. Would you expect that resonance plays a role in this? Explain.