Speed of Sound: Resonance in a Cylinder
In this experiment, we measure the speed of sound based on the resonance that a tuning fork produces over a column of water in a cylinder. Unlike the very direct approach of the previous section, we take advantage of the wave properties of sound to make a much more accurate measurement.
What You Need
- tuning fork of known frequency
- rubber mallet
- closed watertight cylinder (about 15–20 cm tall)—a 1–2 L graduated cylinder will work
- 200 ml beaker (or other container with a spout to pour water into the graduated cylinder)
- quiet room
- Strike the tuning fork with the rubber mallet. Hitting the tuning fork on a hard surface may result in altering its frequency.
- Hold the ringing tuning fork over the top of the graduated cylinder, as indicated in Figure 73-1.
- Place your ear near the top of the graduated cylinder and listen to the sound of the tuning fork.
- Slowly add water to the cylinder and continue to listen. This can be a several-person operation. Be careful not to cause the water to splash, which can distract the listener from hearing the sound of the tuning fork.
- At a certain height, as the water level is raised, the sound of the tuning fork becomes markedly louder. You may need to listen carefully to hear it.
- Once you think you found the resonance, pour out some of the water and confirm that the sound level for the tuning fork becomes lower, and then gets louder again as the water level is brought back up. It should also get lower as the water level is raised above the resonance level. (If you miss the first resonance, continue adding water andyou will hear the second resonance. Using the wavelength for the second resonance will result in a speed of sound that is half the correct value.)
- Determine the frequency of the tuning fork, either by noticing the marking on the tuning fork or by measuring it. You can use an instrument tuner to measure or verify the frequency of the tuning fork.
- Calculate the speed of sound using this equation:
- A more exact expression which accounts for the node of the sound wave not being exactly at the opening of the tube of diameter, d, is:
v = 4 Lf
where L is the length of the air column above the water and f is the frequency marked on the tuning fork.
v = 4f(L + 0.4d)
The accepted value for the speed of sound at 20°C is 343 m/s. The warmer the air, the faster the speed of sound, according to the equation v = 331 m/s + 0.6 T where T is the temperature in degrees centigrade.
To get an idea of the appropriate height needed in the resonant air column for various common tuning forks, you can check the following table. These values do not include the correction factor used in the experiment to account for the diameter of the cylinder. It is possible that someone doing this experiment may not notice the resonance of the fundamental frequency and will continue filling the graduated cylinder until arriving at the resonance for the second harmonic. Table 73-1 serves as a guide to find the column height that produces a resonant frequency.
Why It Works
The resonance occurs when the length of the column produces a natural resonance that is the same as the tuning fork.
One way to think about this is that, at the speed of sound, the sound goes to the bottom of the column and back in the same time as the tuning fork goes through one vibration.
Another way to say this is the frequency of the standing wave that resonates equals the frequency of the tuning fork. The wave equation states that the velocity of a wave equals its wavelength times its frequency. The equation is
where v is the velocity (in m/s), is the wavelength (in m), and f is the frequency (in cycles per second or Hz).
Other Things to Try
Compare this method to the other methods of measuring the speed of sound found in this book.
The speed of sound can be determined by measuring the length of an air column at which a tuning fork establishes a resonance. One-quarter wavelength fits in the air column. Measuring the air column can then determine the wavelength of the sound. This combined with the frequency determines the speed of sound.
Warning is hereby given that not all Project Ideas are appropriate for all individuals or in all circumstances. Implementation of any Science Project Idea should be undertaken only in appropriate settings and with appropriate parental or other supervision. Reading and following the safety precautions of all materials used in a project is the sole responsibility of each individual. For further information, consult your state’s handbook of Science Safety.