# Speed of Sound in Air

There are a number of ways to measure the speed of sound in air. Some use simple equipment, and others use computer- or calculator-based technology. A common, non-technical method uses a tuning fork to set up resonance in a column of air. The length of the resonating air column, along with the frequency of the tuning fork, is used to calculate the speed of sound.

Microphones and computer- or calculator-based technology provide other methods. Experiment 24, Speed of Sound, in our *Physics with Vernier* lab book uses such a method. In this experiment, a microphone records an initial sound and one or more echoes as the sound travels up and down the tube. The time between the initial sound and the echoes, along with the length of the tube, is used to calculate the speed of sound.

**Using a microphone and calculating an FFT**

Logger *Pro* software can be used to perform a Fast Fourier Transform (FFT) analysis on a set of data. The FFT tells you the amplitudes and frequencies of a collection of sine waves that, when added together, would sound the same as the original waveform. An FFT can also be used to measure the speed of sound by determining the fundamental frequency of a column of air. For example, take a 1-m section of PVC and close off one end. Loosely place a cap over the other end. When the loose cap is quickly removed, a low-pitched sound is produced.

If an FFT calculation is performed, the fundamental frequency of the sound can be determined. In this example, the fundamental frequency is 85 Hz. The wavelength of this sound is approximately four times the length of the column. In this example, the speed of sound is 4 * 1 m * 85 Hz, or 340 m/s.

This method can be applied to other columns of air, such as a 20-mL syringe. To try this, push the plunger all the way into the cylinder. Seal the open end with a finger. With the other hand, quickly pull the plunger out of the syringe. A high-pitched “pop” will be heard. Here is a sample set of data showing the raw waveform and the FFT. In this example, the fundamental frequency of the sound is 928 Hz. The length of the syringe is 8.6 cm. Therefore, the speed of sound of the air in the syringe is 4 * 0.086 m * 928 Hz, or 319 m/s. (If we corrected for the effective length of the tube (L=l+0.4 d), we would get a velocity of 348 m/s.)

**Measure the speed of sound with a Gas Pressure Sensor**

The 20-mL syringe mentioned above is provided with our Gas Pressure Sensor. Set up an experiment to collect pressure as a function of time. Set the experiment length to 0.2 s and the sample rate to 10,000 Hz or higher. Set triggering so that data collection begins as the pressure falls. Start the data collection and quickly pull out the plunger. A graph will show a rapidly dropping pressure and a faster return to atmospheric pressure. The region of the graph where the pressure is returning to atmospheric pressure appears to show noise. Zooming in on this region reveals a periodic variation in the pressure. The Gas Pressure Sensor is detecting a change in pressure due to the sound wave traveling up and down the syringe. It should be possible to calculate the speed of sound from this data. The time interval between the first peak and the tenth peak is 0.011 s 2, therefore, the period of the oscillation is 0.0011 s and the frequency is 909 Hz. The speed of sound would be 4 * 0.086 m * 909 Hz, or 313 m/s (which corrects to 342 m/s).

These graphs show data collected with a LabPro and Logger *Pro* software. The experiment can also be done with a TI Graphing Calculator and the DataMate or Physics programs. Since you cannot store as many points on the calculator, the experiment has to be designed to record only the region of interest. This is done by starting the data collection as pressure returns to atmospheric pressure. Set the sample intervals as small as possible. If you are using LabPro or CBL 2, set the interval to 0.0001 s. If you are using the original CBL, set the interval to 0.00164 s. Set the number of data points to 200. Set triggering to occur as the pressure increases and the trigger level reaches 40% of the atmospheric pressure.

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