Randy Worland email@example.com
Department of Physics
University of Puget Sound
1500 N. Warner
Tacoma, WA 98416
Popular version of paper 4aED1
Presented Thursday morning, May 26, 2011
161st ASA Meeting, Seattle, Washington
Musicians who play wind instruments know that tuning is a problem when the air temperature is well above or below normal room temperature, as may occur during outdoor performances of concert bands in the summer and football marching bands in the fall. Instruments from both the brass and woodwind families tend to play sharp when the air is hot and flat when the air is cold.
Wind instruments consist essentially of air columns within which sound waves travel back and forth, reflecting off both ends. These waves are set into motion by vibrating lips in brass instruments, and by vibrating reeds or oscillations of air blown across an aperture in woodwind instruments. The pitch that we perceive when a note is played is determined by the frequency of the sound waves that can resonate in this manner within the air column.
The rate at which the sound waves travel back and forth along the length of the instrument depends on both the tube length and the speed of the waves. This rate (i.e. the frequency) increases for a shorter tube length, and also increases if the wave speed is greater. Thus, with a fixed wave speed, a longer tube will produce a lower frequency, while a shorter tube produces a higher frequency. This is reflected in the observation that longer instruments (such as tubas) produce low notes, and shorter instruments (e.g. piccolos) produce high notes. On a given instrument, different notes can be played by increasing or decreasing the effective length of the instrument. This can be accomplished by depressing valves to add tubing or by uncovering finger holes to shorten the air column.
The other factor that determines the frequency produced by a wind instrument is the speed at which the sound waves travel. Although typically about 343 m/s (at room temperature), the speed of sound does vary slightly with the temperature of the air, increasing as the temperature rises and decreasing as the air becomes colder. Thus, with the length held constant, a wind instrument resonates at a higher than normal frequency (sounding sharp) when the weather is hot, and at a lower than normal frequency (sounding flat) when the weather is cold. The individual instruments must be tuned by the player to compensate for this effect when the ambient temperature is hotter or colder than normal.
A simple and inexpensive demonstration of this air temperature effect has been developed that can be used in classes of various levels. Three PVC tubes are cut to identical lengths and an end cap is glued to one end of each tube. The tubes produce a single pitch when air is blown across the open end, as in blowing across the mouth of a bottle or playing a flute. To vary the air temperature, one tube is placed in a beaker of ice water (T = 0 oC) and another in a beaker of hot tap water (T = 40 oC). The third tube remains at room temperature (T = 20 oC) to serve as a reference. After a few minutes, the three tubes are played and the resulting pitch variations are observed. The ice water tube sounds flat in comparison to the reference tube, while the hot water tube sounds sharp. Although the speed of sound varies only slightly over this temperature range, our ears are very sensitive to small frequency differences, and the tubes are clearly heard as being out of tune with one another.
Video 1. Video clip showing three identical PVC tubes being played by blowing across the open end. One tube has been cooled in ice water, one has been warmed in hot tap water, and one serves as a room temperature reference. Note that the pitch of the cold tube sounds flat, while the pitch of the hot tube sounds sharp in comparison with the reference tube.
More extreme temperature variations, resulting in more dramatic pitch changes, can also be achieved in the lab. For a lower temperature the PVC tube can be cooled in liquid nitrogen, which is approximately 200 oC below room temperature. For a higher temperature the tube can be placed in water heated close to 100 oC on a hot plate. The air inside the tube does not reach the temperature of the bath in either case, but does vary significantly above and below room temperature. Note: these versions of the experiment can be dangerous and should only be done by the instructor.
Video 2. Video clip showing a PVC tube played after being heated in water on a hot plate. The heated tube produces a higher pitch than the identical reference tube at room temperature.
Video 3. Video clip showing a PVC tube played after being cooled in liquid nitrogen. The tube containing cold air produces a much lower pitch than the identical reference tube at room temperature. (Note that the tubes used here are slightly longer and larger in diameter than those used in the other video clips.)
For a more quantitative project, students can measure the frequencies produced by the tubes in the laboratory and calculate the effective temperature of the air in the tube, based on the known dependence of the speed of sound on temperature. Students can also perform calculations to address the common misconception that the tuning problem is caused by thermal expansion and contraction of the wind instruments. Although length changes do occur as the temperature is varied, the effect can be shown to be extremely small, with a predicted frequency change in the wrong direction.In conclusion, the demonstration provides a simple and low cost illustration of the effect of air temperature on wind instrument tuning. It can be adapted to suit a wide variety of class levels and can be expanded to include a quantitative experimental component in addition to the qualitative presentation described here.