The Effect of Temperature on Sound Frequency

The sound frequency of a woodwind instrument is affected by various factors, including mouth embouchure of the player (shape of mouth) and equipment being used. Temperature is one of the factors that a player does not have control of, leading to adjustments needed to be made by the player in order to reduce the impact made by temperature. This interests me because as a woodwind player myself, I am interested in seeing how much of an effect does temperature really have on the sound frequency of a pitch produced by an instrument. I know that temperature does not directly affect the pitch, but rather it changes the speed of sound in the instrument. Heat is a form of kinetic energy, and as it increases, so do the movement of molecules. This is what allows sound waves to travel more quickly. The equation used to find the speed of sound is the following:

v = 331m/s + 0.6m/s/C * T

Luke Corwin (2007) also hypothesized an equation on the change of an instrument’s pitch due to temperature:

This information available to me was fascinating and I wanted to perform an experiment where I was able to view the results directly and see the effects of temperature on an instrument that I was familiar with. This is what led to the conduction of this experiment.

Statement of Problem: top

The purpose of this investigation is to determine the impact of temperature on sound frequency based on the pitch of a musical instrument.

Hypothesis: top

An increase in temperature will affect the pitch of a wind instrument, resulting in a higher sound frequency due to a faster speed of sound.

Materials: top

❏ Alto Saxophone

❏ Tuner App on Smartphone

❏ Thermometer

❏ Space Heater

❏ Fan

Variables: top

In my experiment, I will see how temperature impacts the sound frequency (Hz) of the pitch of the alto saxophone. I will be comparing each sound frequency to 440 Hz, the general tuning standard for musical pitch. The variable that will be manipulated is the temperature, which will be the independent variable of the experiment. The dependent variable that I will be measuring is the frequency of the pitch produced by the instrument.

Procedure: top
I first set the temperature of the instrument to 30° F by having the mouthpiece next to a fan and let it reach the desired temperature. I then picked up the instrument and had an assistant hold the smartphone up to the horn with the tuning app running to pick up the pitch. I played an F sharp (440 Hz) and had the pitch recorded, along with the initial frequency that it produced. Once that was recorded, I repeated the same procedure, only to raise the temperature by 5° F. This was repeated until temperature reached 90° F. The only variable that was manipulated was temperature.

Data and Graphs: top

Temp (F)	Frequency (Hz)
30	451
35	455
40	456.4
45	456.5
50	458.2
55	458.4
60	461.7
65	468.3
70	467.8
75	470
80	472.1
85	473.6
90	473.9

Text | Excel

As the temperature increased, so did the sound frequency, getting higher and higher.

The percentage error was then calculated for each data point, comparing it with the control of 440 Hz. The following equation was used:

Percentage Error: top

Temp (F)	Percentage Error (from 440 Hz)
30	2.47
35	3.35
40	3.66
45	3.68
50	4.05
55	4.1
60	4.81
65	6.23
70	6.12
75	6.59
80	7.04
85	7.36
90	7.42

With the temperatures rising, the percentage error increased along with it. This meant that the pitch was less accurate the higher the temperature was and was not in tune as it should have been.

Potential Errors: top

Even though this experiments able to successfully show that higher temperatures lead to higher frequencies, there are still potential errors present in the experiment that could have to lead to misleading data. One area that could be improved is how data was collected. A phone was used with a tuner app to collect the pitch of the saxophone. Had a microphone or more accurate form of collecting data been used, a more accurate frequency would have been collected. Another potential source of error is the fact that only initial pitch was collected. This meant that the pitch was not given time to steady and become stable. The reason for collecting initial pitch was to make sure that other factors did not affect the sound frequency, such as the shape of the mouth or the speed of air. A potentially significant source of error is the room that the experiment was conducted in. The temperature was controlled to the best of my extent, yet it was still difficult to obtain an exact temperature. A way to improve this would be to conduct the experiment in a controlled environment where the temperature is in complete control. Finally, the interiors of the saxophone were something out of my control, where a lot of the speed of the air is affected.

Conclusion: top

Overall, the experiment was able to show how the speed of sound is impacted by a higher temperature, leading to a higher increase in frequency. It would be interesting to see how a brass instruments pitch is impacted by temperature compared to a wind instrument given the fact that their interiors work much differently when looked at side by side. This experiment would be stronger if more trials were conducted, and be able to see what frequency was more common for each temperature point. It was great to see the direct impact that temperature had on a musical instrument, and leads me to wonder what other experiments could be conducted to continue researching the relationship between temperature and sound.

Bibliography: top

Corwin, L. A. (2007). Why does the pitch of a brass wind instrument increase when temperature increases?. Informally published manuscript, Ohio State University Department of Physics

“Temperature and the Speed of Sound.” NDE Ed, NDT Resource Center, www.nde-ed.org/EducationResources/HighSchool/Sound/tempandspeed.htm.

Worland, Randy. “ASA Lay Language Papers 161st Acoustical Society of America Meeting.” Acoustics, Acoustical Society of America, 26 May 2011, acoustics.org/pressroom/httpdocs/161st/Worland.html.

Additional Links: top

https://physics.info/sound/ - Very in depth website on the nature of sound.

http://hyperphysics.phy-astr.gsu.edu/hbase/Sound/souspe.html - Speed of sound in air calculator. Not entirely accurate, but gives a good view on how it works.

www.nde-ed.org/EducationResources/HighSchool/Sound/tempandspeed.htm - Gives some in depth research on how temperature impacts frequency.

https://courses.lumenlearning.com/physics/chapter/17-2-speed-of-sound-frequency-and-wavelength/ - Some more in depth lessons on the speed of sound.

http://www.sengpielaudio.com/calculator-waves.htm - This website is a more in depth calculator on the acoustic calculation of a wave when the temperature and frequency is known.