Resonance In a Water Column & the Speed of Sound
When a standing wave is set up in a resonance cavity of some kind, like the closed ended pipe you will use in this lab today, the standing waves will only occur at certain multiples of the wavelengths of the vibration which produces the waves. In this lab, when standing waves are set up inside the resonator, an amplification of the sound producing the vibrations will be observed. For a closed tube resonator, the first standing wave occurs when ¼ of a wave overlaps inside the space. The length of the resonance cavity at this point will have the following relationship with the wavelength at this point:
If the frequency of the vibration is known (in this lab the frequency will be stamped on the tuning forks used to produce the vibration), one can easily calculate the wave speed using
Procedure:
1. Carefully fill the cylinder with water to within a few centimeters of the top.
2. Make sure you hold the string connected to the hollow tube so that the tube does not sink below the water. If this happens you will have to empty out all the water and start again.
3. Strike the tuning fork (ON SOMETHING SOFT!) and hold it perpendicular to the top of the tub, slowly raise the tube out of the water until a resonance amplification is heard. You will know it when you hear it! You may need to strike the tuning fork multiple times as you raise the tube.
4. Record the length of the tube, L, at this point.
5. Calculate the wavelength and the speed of the sound wave with this data.
6. Repeat using 2 additional tuning forks of different frequencies.
7. (optional extension) Repeat the experiment using hot water.
Data:
Tuning Fork 1
f = ______L = ______ = ______v = ______
Tuning Fork 2
f = ______L = ______ = ______v = ______
Tuning Fork 3
f = ______L = ______ = ______v = ______
Extend:
Select one of your tuning forks that produced standing waves at the shortest L. Go back to the point where resonance was heard. Strike the tuning fork and continue to raise the tube higher and higher. Do you hear the amplification of the sound wave at another height? Where does this occur and what mathematical significance does this value of L have (hint: play around with your numbers…you already know the speed of sound).
Drawing Conclusions:
· On your lab report, show a sample calculation complete with equations and substitution.
· Write a general statement that describes what happened to create the amplified sound when the tube length was close to ¼ of the wavelength of the vibration.
· Why did the resonance occur at ¼ of the wavelength?
· Did the values of the velocity of the sound waves change much with different tuning forks? What was your average speed?
· Assume that the speed of sound at room temperature is 343 m/s. Calculate the accuracy of your results by doing a percent error estimation on your average velocity.
· Why does sound of different frequencies travel at the same speed?
· Give a real life example that proves that sound waves travel at the same speed regardless of frequency.
· We know that air of different temperatures has different densities. This will change the speed at which the sound wave can propagate through the air. Design a similar experiment which would allow you to determine the speed of sound for air at different temperatures.