Physics of Sound Projection in the Didgeridoo

A description of the sound production in the didgeridoo as a single open end, single closed end pipe instrument.

The didgeridoo is a cylindrically shaped instrument with two openings. One end is closed off tightly by the didgeridoo player’s mouth creating a pipe with an open and closed end. The physics of sound waves created inside a pipe with one open end are very different from that of a pipe with two open ends. Authentic and aboriginal didgeridoos are carved from termites and thus have imperfections in the inner tube. These imperfections give each didgeridoo its distinctive sound. Modern day didgeridoos, however, do not have these imperfections and can be made to uniform sound and shape. Most often the diameters of each end of the didgeridoo are different. The physics of a pipe with one open end will be investigated here along with various factors that can be altered to change the didgeridoo’s sound.
The didgeridoo is played similar to many brass instruments in which the lips are vibrated to create areas of high and low pressure within the tube. The sound waves travel down the inside of the didgeridoo and exit the open bottom end. This variation in pressure causes the instrument to vibrate air molecules at the end of the tube. Varying frequencies of standing waves are produced creating an audible sound or ‘drone’.





In the pipe, standing sound waves are created and a pressure node and a displacement anti-node are formed at the open end of the instrument. Since the sound waves travel in air, the pressure at the open end of the tube is held fixed at Patm and cannot oscillate. The standing wave produced within the tube is a combination of different frequencies called pitch.
The standing waves created by such a tube are characterized by the equation:
λn = 4L / n
where n = 1, 3, 5, . . .

The frequencies of standing waves in the tube are characterized by the equation:
ƒ = n * (vsound / 4L)
where n = 1, 3, 5, . . .





The didgeridoo produces odd-numbered harmonics whereas a tube with two open ends produces even-number harmonics. When these harmonic frequencies are achieved, the instrument produces a strong and vibrant tone known as a drone.
The equations above have many implications. For instance, the fundamental frequency can be altered by changing the length of the didgeridoo. Longer didgeridoos have a higher wavelength and thus a lower pitch when played. In comparison, shorter didgeridoos will have shorter wavelengths and higher pitches. Unlike woodwind instruments, the didgeridoo cannot produce different pitches; Different sounds must be created by altering the sound waves that enter the instrument through use of the vocal chords, lips, cheeks, etc.





Useful Links to Visualize Standing Waves in an Open-Closed Tube:
1. http://www.physics.smu.edu/~olness/www/05fall1320/applet/pipe-waves.html
2. http://openlearn.open.ac.uk/file.php/3524/normalModes.swf