Optional Unit V: Sound
B. Transmission of Sound

2. Speed of Sound

Key Concepts

The speed of sound varies in different types of media. Generally, sound travels fastest in solids, slower in liquids, and slowest in gases.

The temperature of air (or other gases) affects the speed of sound.

The speed of sound in air (accurate only over a relatively small range of temperatures) can be determined by:

v = (331 + 0.610t) m/s where t is the temperature in degrees Celsius, or v = 20.0 ms^-1K^-½, where T is the temperature in Kelvin.

Because sound travels slowly (compared to light), experiments to determine the speed of sound can be performed with relative ease.

Historically, the speed of sound was measured accurately long before the speed of light was determined.

Learning Outcomes

Students will increase their abilities to:

1. Explain that the speed of sound varies in different types of media.

2. Make generalizations comparing the speed of sound in solids, liquids, and gases.

3. State that the temperature of air (or any other gas) affect the speed of sound in that medium.

4. Calculate the speed of sound in air at different temperatures.

5. Solve problems relating to the speed of sound in air, or any other given medium.

6. Suggest an experimental procedure which could be used to determine the speed of sound.

Teaching Suggestions, Activities and Demonstrations

1. Using an adjustable air column and several tuning forks with different frequencies, determine the speed of sound in air using resonance techniques. If a water column is used to adjust the height of a closed-end air column, better results may be obtained if the water is allowed to reach room temperature before being used for the experiment.

2. Resonance columns can be improvised from cardboard cylindrical mailing tubes, or plastic golf club protectors. To make the columns adjustable, suspend a hooked mass inside the tube. The mass may have to be wrapped with several layers of tape so that its diameter is just slightly smaller than the inside diameter of the tube.

3. To illustrate that the speed of sound changes in different gasses, fill several balloons with different gasses - helium, oxygen, carbon dioxide - whatever is available or can be prepared.

   Attach a whistle or a horn to the end of the balloons and release the gas. Repeat for the different gasses. Tape record the sounds produce and replay them for further analysis. If gasses such as hydrogen or acetylene are used, do not place the balloons near hot objects.

4. Search for exceptions to the generalization that sound travels faster in liquids than in gases, and faster in solids than in liquids.

5. Experimentally determine the speed of sound in air using an echo sounding technique, a resonating air column, or some other feasible method.

6. If helium gas is available, demonstrate to students the change in pitch that occurs when you inhale the gas and try to speak. This popular nineteenth century parlour trick can have some amusing results. Have students try to explain why the change in pitch occurs. (Never try to inhale a sample of helium gas from a pressurized container. Instead, put some of the gas in a balloon and inhale the gas from the balloon. Do not use hydrogen gas for this demonstration.)

7. The Newton-Laplace equation for the speed of sound in a gas is , where P is the pressure, = density, and is the ratio of the specific heat of the gas at a constant pressure over the specific heat at a constant volume.
   
   Gamma () is about 1.67 for monatomic gases, 1.40 for diatomic gases, 1.30 for triatomic gases, and in the range of 1.2 to 1.1 for polyatomic gases.

   Applying the Ideal Gas Law, the equation for the speed of sound in a gas becomes , where v represents speed, is the specific heat ratio, T is the temperature in Kelvin, k is Boltzman's constant, m is the mass of one molecule, R is the ideal gas constant, and M is the molecular weight of the gas.

   The speed of sound in a gas depends on the temperature, molecular weight, and molecular structure, but not on the pressure of the gas. For a given gas v .