HPP Activity 51v2
Exploration
Your instructor will demonstrate what happens to the human voice when normal air is replaced by helium. If the instructor cannot demonstrate this then listen to the audio files vowels.norm.8000.wav and vowels.helium.8000.wav.
GE 1.
1. Describe how you think the voice changes when air in the vocal tract is replaced by helium.
Invention
Vowel sounds in speech are determined by the shape of the vocal tract. The shape determines allowed resonant frequencies. These frequencies are determined by the standing waves that can be supported by the vocal tract.
The simplest model of the vocal tract would be to picture it as a single cylindrical tube with one closed end, at the glottis, and one open end, at the mouth. Such a tube can support standing waves. The strongest frequencies present in the sound emitted from the mouth are called formants . In our model, the formant frequencies correspond to the standing wave frequencies in the tube. The first two formants would correspond to the first two possible standing waves in the tube.
Some vowel sounds require a vocal tract shape that is not well described as a single cylinder.
The next simplest model is that the vocal tract has two cylinders of possibly different lengths.
Again, we imagine each tube to have a closed end, the narrowest end, and an open end, which would be the widest side. Figure 1 shows an outline of the vocal tract and the corresponding two tube model.
Activity Guide

2010 The Humanized Physics Project
Supported in part by NSF-CCLI Program under grants DUE #00-88712 and DUE #00-88780

HPP Activity 51v2 2
Figure 1. Two tube model of the vocal tract.
For this model, the first two formants are determined by the simplest standing wave being set up in each of the two tubes.
Application
We will describe the formants present in several vowel sounds, observe what happens to them when we replace air by helium, and then determine for each vowel sound which model, the one tube or two tube model, best describes the vocal tract when the sound is produces.
Open up the file vowels.normal.8000.wav with the sound editing program available to you.
Make sure the application is in the sound spectrogram display mode. If such an application is not available, use the print out of the sound spectrogram.
GE2.
1. Identify the first and second formants for each vowel sound in the file.
Look for the frequency of the darkest regions. This indicates the largest intensity in the FFT.
If you are using the sound spectrogram application, just use the mouse to locate the formants and read the frequency off the frequency window.
If you are using the printouts of the sound spectrogram, measure the distance from the otom of the spectrogram to the region of interest and use a conversion factor to go from length to frequency. Note that the frequency range of the entire spectrogram is 4000 [Hz] on the printout.
Fill in the table below:
Activity Guide

2010 The Humanized Physics Project

HPP Activity 51v2
Vowel
[i] (heed)
1 st
Formant [Hz] 2 nd
Formant [Hz]
[I] (hid)
[u] (hood)
[E] (head)
[a] (hod)
[ae] (had)
Let’s determine which model, the one tube or two tube, works best for each vowel sound.
GE3.
1. Write down the relationship between sound speed, column length, and frequency for standing wave patterns in a tube with one closed end and one open end.
2. If the one tube model is correct then what would the second formant frequency be in terms of the first?
3. Fill in the table below with the measured first formant and the predicted second formant using the 1 tube model.
Vowel
[i] (heed)
[I] (hid)
[u] (hood)
[E] (head)
[a] (hod)
[ae] (had)
1 st
Formant [Hz] Predicted 2 nd
Formant [Hz]
4. For which vowel sounds does the one tube model work?
5. Using the standing wave equation, solve for the length of the tube in terms of sound speed and frequency. Express symbolically.
Activity Guide

2010 The Humanized Physics Project
3

HPP Activity 51v2
6. Assuming either the one tube or two tube model, whichever works best for the sound, calculate the length of the relevant tubes using the measured formant frequencies. Use 340. [m/s] for the speed of sound.
Vowel
[i] (heed)
[I] (hid)
[u] (hood)
[E] (head)
[a] (hod)
[ae] (had)
1 st
Length [m] 2 nd
Length [m] Total Length [m]
7. An average vocal length for an adult male is about 17 [cm]. While there will be some changes in length as different vowel sounds are made, we do not expect the changes to be more than a few centimeters. How well does our model predict the total length of the vocal tract?
Let’s see what happens to the formants when we introduce helium.
Open up the file vowels.helium.8000.wav with the sound editing program available to you.
Make sure the application is in the sound spectrogram display mode. If such an application is not available, use the print out of the sound spectrogram.
GE 4.
1. Identify the first and second formants for each vowel sound. Fill in the table below.
Vowel
[i] (heed)
1 st
Formant [Hz] 2 nd
Formant [Hz]
[I] (hid)
[u] (hood)
[E] (head)
[a] (hod)
[ae] (had)
4
Activity Guide

2010 The Humanized Physics Project

HPP Activity 51v2
2. Generally, what is happening to the formant frequencies when helium is introduced into the vocal tract?
3. What is the primary determinant of the opening/closing frequency of the glottis in the larynx?
4. How does the speed of sound in helium compare with the speed of sound in normal air at room temperature?
5. Use your measured formant frequencies and your calculated tube lengths to estimate the speed of sound in the vocal tract. Find an average and uncertainty.
6. How does your calculated sound speed in the vocal tract with helium compare with the accepted speed of sound in helium?
7. Do you think all of the air in the vocal tract was replaced by helium in this experiment?
5
Activity Guide

2010 The Humanized Physics Project