What frequencies does the larynx produce?

Transcription

1 HPP Activity 48v3 What frequencies does the larynx produce? Exploration Open up the DataStudio file with the microphone setup: SoundBasic.ds. Make the oscilloscope view active. Press Start and hum an ahhh sound into the microphone. Change the time/div setting until you can get several cycles of the signal to display. GE Do you think the sound wave you produce with your humming has a definite frequency associated with it? What evidence do you have for your opinion? 2. Now display the signal generator output on the oscilloscope. You may have to change the time/div setting to get several cycles to display. The signal generator should be producing a pure sine wave. How does the sine wave shape compare with the humming sound wave shape? A mathematical procedure called the Fourier transform can give information about the frequencies present in a signal. You can get the computer to perform a Fourier transform on your data by setting up a Fast Fourier Transform, or FFT, display. Close the oscilloscope display. Create an FFT display of the microphone voltage. Set the sample rate to 10,000 samples/s on the FFT display. Click the Start button. Start humming. When you have a stable signal click the Stop button. GE What frequencies are strong in your "ahhh" sound? 2. Obtain a Fast Fourier Transform of the sine wave signal. What frequencies are present in this signal? Supported in part by NSF-CCLI Program under grants DUE # and DUE #

2 HPP Activity 48v Start humming the "ahhh" sound again and form the FFT of this signal. Without changing the pitch of your voice, change the sound from "ahhh" to "eee". What happens to the frequencies shown in the FFT? 4. Perform an FFT analysis of the sound produced by the larynx model. Does it produce one or multiple frequencies? 5. What might you do to the larynx model to change the intensities of the frequencies it produces without changing the actual frequencies? Would changing the tension of the latex strips work? Can you think of anything else? 6. Using available materials, try your ideas. Describe the results here. We have two problems to study related to the experiments you just did. The first problem is to understand why the vocal folds produced a series of almost equally spaced frequencies. The second problem is to understand why many of the produced frrequencies disappear or have reduced intensities once the sound wave interacts with the oral/nasal cavity. The two problems are related and can be at least partially understood in terms of a concept called standing waves. We will develop this idea now. Obtain a slinky and "fix" one of the ends so it cannot move. You can do this by either placing it in a clamp or having someone hold it. Stretch your whole Slinky to its full length so it hangs freely in the air, fixed at one end and in your hand at the other end. Shake the non-fixed end of the slinky to create a standing wave. Practice until you are able to produce standing waves with two nodes (at the two ends), three nodes (two at the ends and one in the middle), and four nodes (two at the ends and two between the ends). There are some sample pictures below to guide your work. Nodes at the ends Nodes in the middle & at the ends GE Determine the frequency of the side to side (or up and down) oscillations necessary to create each of the following three standing waves:

3 HPP Activity 48v3 3 a. 2 nodes (one at each end); find frequency = f 0 b. 3 nodes (at the ends and one in the middle); find frequency = f 1 c. 4 nodes (at the ends and two between the ends); find frequency = f 2 Sketch the relevant standing wave patterns and record your frequency values. 2. Write the mathematical relationship between the frequencies you found above. What would you expect for the frequency of f n? 3. Stretch half of your Slinky about the same length as the whole Slinky above. What is now different from the activity you did above? How would you expect that to change the behavior of the system? Explain. 4. After having stretched your half Slinky to the appropriate length and keeping one end fixed, determine and record the frequency of the oscillations necessary to create a standing wave with: a. 2 nodes (one at each end); find frequency = f 0 b. 3 nodes (at the ends and one in the middle); find frequency = f 1 5. Write the mathematical relationship between the frequencies you found in question #4. What would you expect for the frequency of f n? 6. Compare your answers to questions 2 and 5. Invention

4 HPP Activity 48v3 4 Let's try to find a relationship between the length of Slinky L and the allowed wavelengths. GE Given that the endpoints of the Slinky must remain still (nodes), why is it not possible to place a wave with any arbitrary wavelength on the string? 2. What is the simplest standing wave pattern that could be fit on the Slinky? 3. What is the relationship between the Slinky length L and the wavelength λ for this case? 4. What is the next simplest standing wave pattern that can be fit on the Slinky? 5. What is the relationship between the Slinky length L and the wavelength λ in this case? 6. Try to develop a general formula for the allowed wavelengths for standing waves on the Slinky with both ends fixed. Check your result with the instructor. 7. Use your result from question 6 to write down a formula relating the allowed frequences for a standing wave and the length for a Slinky with both ends fixed. Application GE 5. Let s try to relate standing waves on the Slinky and string to the sound frequencies produced by the vocal folds. 1. Do you think the vocal folds can vibrate with any frequency? Explain your reasoning or evidence.

5 HPP Activity 48v In what ways might the vocal folds be like the Slinky used in the previous experiment? 3. Develop a hypothesis to explain the frequency pattern observed when you made the ahhh sound. Application GE 7. Standing Sound Waves and The Speed of Sound. Obtain a long glass tube with water reservoir tuning fork rubber mallet Get the instructor to show you how to set up a standing wave in an air column. 1. Do you think that the open end of the tube is a node or an antinode? 2. Do you think that the water surface is a nod or an antinode? 3. The standing sound wave can be represented as a pressure versus position graph. Draw the simplest possible standing wave pattern that could fit in the air column. 4. What is the relationship between wavelength and tube length L for this case. 5. What is the next simplest standing wave pattern that can fit it the tube? 6. What is the relationship between wavelength and tube length L for this case?

6 HPP Activity 48v Develop a general formula for the the relationship between wavelength and tube length for standing waves with one end fixed and one end free. Check you result with the instructor. 8. Use the result from question 7 to find a formula relating allowed frequencies and the length of the tube. 9. Devise an experiment for measuring the speed of sound in air using standing wave observations. Describe your plan here. 10. Record your data. 11. Analyse your data. What is your estimate of the speed of sound in air?