Course:PHYS341/2022/Project33

The Clarinet

How does it work?

Basic info

The clarinet is a woodwind instrument that is played with a single reed. The frequencies of the clarinet are similar to those that would be produced by a closed-open cylindrical tube. (f, 3f, 5f, 7f) The holes and keys are used to change the length of the tube to produce different notes and frequencies.

How sound is produced

The player creates higher pressure in the mouth than is present inside of the instrument. The pressure inside the instrument varies with standing wave oscillations in the tube. In response to these pressure variations, the reed oscillates up and down, opening and closing the opening. The timing of this opening and closing reinforces and drives the oscillations in the tube.

As the pressure in the instrument increases, there is a net downward force on the reed. This opens the reed requiring more force from the air in the mouth.

As the pressure in the instrument decreases there is a net force upwards on the reed. This causes the reed to close, requiring less force from the mouth.

The net result of these reed oscillations is that the air in the mouth pushes more when the pressure inside the instrument is high and pushes less when the pressure inside the instrument is low. The reed vibrates with the same period as the standing waves inside a closed open cylindrical tube.

Side note:

The wavelength corresponding to any given frequency in a closed-open tube is four times the length of the instrument from the mouthpiece to the first open hole. For Flutes and oboes, which are similar to an open-open cylindrical tube, the wavelength is only two times the length of the tube. This is why, although they are similar in length, the clarinet is able to play almost a full octave lower than the flute or the oboe.

Upper register

In order for the vibration in the instrument to continue, the frequency of vibration of the reed must be higher than the frequency of resonance inside the instrument. This is why the higher notes on a clarinet are sometimes more difficult to play. Even if the correct fingering is used for these notes there will be no sound produced unless the frequency of the reed is high enough. This is where the mouth of the player becomes a part of the instrument. Players are actually able to control how much of the reed is actually vibrating by controlling where on the mouthpiece the reed makes contact. They do this through the control of their embouchure. (embouchure: the position and use of the lips, tongue, and teeth in playing a wind instrument)

Soft vs. loud playing

When playing softly the reed oscillates only a small amount. The forces involved obey Hooke’s Law and are nearly simple harmonic motion. The sound produced is almost a pure tone. When playing softly there is a much larger oscillation of the reed. The reed completely blocks the mouthpiece for part of the period. The result is a complicated time graph with a rich spectrum.

Tuning

Parts of the clarinet can be adjusted to change the frequencies produced by the clarinet. For example, the “barrel” of the clarinet (the piece directly below the mouthpiece) can be pulled out (to produce a lower frequency) or pushed in (to produce a higher frequency). This is usually used when there is a change in the environment such as temperature. It allows the player to change the length of the instrument as the temperature of the instrument changes.

Appearance of Notes in Different Octaves

For this part of the project I played two notes on the clarinet. The two notes played were both the note C but played in different octaves.

Spectrum of Frequencies

The Lower C as seen in the spectrograph pictured has a fundamental frequency around 262 Hz. This frequency most closely corresponds to a C4 which has a frequency of 261.63Hz.

This is the spectrum of frequencies produced when playing the note C on the clarinet in the lower register.

The Upper C as seen in the spectrograph has a fundamental frequency around 524 Hz. This frequency most closely corresponds to a C5 which has a frequency of 523.25Hz. This shows that going up an octave doubles the produced frequency.

This is the spectrum of frequencies produced when playing the C note on the clarinet in the upper register.

Both spectrums correspond to what is expected from a closed-open cylindrical tube: there are spikes at the expected frequencies (f, 3f, 5f, 7f, etc.) It appears that the lower C has a wider spectrum of frequencies than the upper C possibly because of how quickly the frequency increases when the fundamental frequency is already so high.

Time Graphs

The time graph as well shows a more complicated waveform for the lower C. This is due to the increase in frequency that corresponds to the increase in pitch.

Time Graph for the note C played in the lower register on a clarinet.

Time graph for the note C played in the upper register on a clarinet.

References

1. Clarinet acoustics - NIU - clarinet study with Greg Barrett. Northern Illinois University. (n.d.). Retrieved April 2, 2022, from https://www.niu.edu/gbarrett/resources/acoustics.shtml#:~:text=Clarinet%20acoustics%20are%20determined%20by,bore%20produces%20the%20clarinet's%20sound.
2. Merriam-Webster. (n.d.). Embouchure definition & meaning. Merriam-Webster. Retrieved April 2, 2022, from https://www.merriam-webster.com/dictionary/embouchure
3. The origins of the clarinet the modern clarinet. The Origins of the Clarinet：The modern clarinet - Musical Instrument Guide - Yamaha Corporation. (n.d.). Retrieved April 2, 2022, from https://www.yamaha.com/en/musical_instrument_guide/clarinet/structure/structure002.html
4. Tuning. Frequencies of Musical Notes, A4 = 440 Hz. (n.d.). Retrieved April 2, 2022, from https://pages.mtu.edu/~suits/notefreqs.html