Tomonaki Inuoe, Ian Jacobs: 2000
Have you ever wondered what sound waves would look like if you could see them? Bending as they go through doorways, scattering and reflecting from everything around you. The world would be full of ripple patterns.
Just like water waves, a sound wave has wavelength, speed, amplitude, and frequency. We associate amplitude with loudness and interpret frequency as pitch.
Imagine tha someone is hammering nails into wood, a distance, do from where you are standing. Watch and listen as the hammering frequency is increased. At some point, the bang is heard as the hammer reaches the top of the back swing. When this happens, the speed of sound is do multiplied by half the hammering frequency. To find the speed of sound in air more accurately, the time for an echo to return from a wall at a known distance can be measured. The principle is the same. Measure the delay time and find the velocity as distance over time.
All students learn the wave equation:
The wave equation is the relationship between the wavelength and velocity of any wave, and the frequency of the wave generator. Traveling waves are discussed elsewhere. Standing waves arise when traveling waves are reflected between two boundaries.
Studying a standing wave in a pipe is a convenient way to find the speed of sound. The frequency and the distance between nodes are measured. The distance between nodes is half the wavelength. Substituting frequency and wavelength in the wave equation gives the velocity of the component traveling waves.
Both methods give the correct speed but they are not accurate enough to find the speed-temperature relationship from 20-30°C.
The speed of sound as a function of temperature is given in the Handbook of Physics and Chemistry as....
v = 331.5 + 0.6 T ... where v is in meters per second and T is the temperature in °C
Tomoaki Inoue, ISB (98-00), recommends the following method.
Data Logger Pro (from http://vernier.com) allows two or more probes to be connected a computer at the same time. In this case a Macintosh 6400 is used with a distance probe and fast response temperature sensor also from Vernier.
Data
A motion detector was put on a table close to a temperature probe.
The computer was set to calculate the distance from the probe to the ceiling. The actual recorded measurement is the time delay for the return echo. To improve the echo a hard plastic panel was fixed to the ceiling. The formula for calculating the speed of sound from distance and time measurements was entered into Data Logger.
Bangkok has a tropical climate and the laboratories at ISB are air conditioned. The air conditioners were turned on for half an hour and then turned off. Two graphs were plotted as the room warmed up. The ceiling appears to become lower as the temperature increases! As the room temperature rose, the air quickly became stratified with warmer layers closer to the ceiling. The temperature measurement at table height for higher temperatures was too low, leading to non linear graphs.
To eliminate this problem the measurements were repeated for horizontal sound propagation. As an added precaution, the calibration of the distance probe was checked. Entering the revised value of do with delay times for horizontal propagation gave the expected linear graphs. The values of the constants are (within errors) the same as those given in the Handbook of Physics and Chemistry: ie....
... where T is the temperature in °C
Editor's comments
This demonstration extends what could previously be done in a school laboratory. It is an excellent example of the power of modern equipment. The temperature-speed relationship is introduced experimentally which improves the rigor of an introductory course. Not everyone has air conditioners but similar results can be obtained with room heaters in a temperate climate and the region around zero degrees Celsius can be reached, to confirm that the relationship is in fact linear, over the entire room temperature range.