The Blue Man Group is a unique theatrical and musical organization. They take the everyday element of music and put a spin on it by playing with PVC pipes. Their performances provide much enjoyment to the audience, but the creators’ thinking behind the instruments are quite complex. For our project, we decided to make a xylophone and drumbone like the ones the Blue Man Group uses. However, before we could build the instruments, we needed to find out how sound waves work so that we could build them correctly to produce the desired notes.
Before figuring out how to construct the
xylophone and drumbone, we needed to find out how sound waves work. A sound
wave is a pressure disturbance that travels through a medium by means of
particle interaction. Sound waves are made of evenly spaced air molecules. The
term “sound wave” is actually a misnomer. Instead of a physical wave, sound is
produced by vibrating particles. When something vibrates, air molecules
continue to bump into each other in a longitudinal movement, from regions of
high pressure (compression areas), along with areas of lower pressure
(refraction areas). This is illustrated below.
Sound pressure waves are often illustrated as
sine waves because it is easier to visualize their properties. The compression
points correlate with the crest of a sine wave, and the refraction points with
the trough of the wave. Sound waves, like sine waves, have amplitudes,
wavelengths, and frequencies. Amplitude is measured in decibels, which tells
how loud the sound is. Different pitches are caused by different spacing of, or
distance between the waves, or wavelengths. The closer together the waves are
the higher the sound. The farther apart the waves are, the lower the note. We
found a formula for wavelengths, written below.
λ=wavelength of a
sound wave,
vw= the speed of the wave
f= frequency of
the wave
The frequency is also known as the pitch of the note, often measured in Hertz. One Hertz is equivalent to one vibration per second. Therefore, a note of 440 Hertz makes a higher pitch than one with only 200 Hertz.
Here is another diagram that shows how sound waves look like sine waves.
Another thing that needs to be considered
when building our instruments is the speed of sound. At normal atmospheric
pressure and a temperature of 20 degrees Celsius, a sound wave will travel at
approximately 343 m/s; this is approximately equal to 750 miles/hour.
The equation above for wavelengths can be
converted to figure out speed.
Speed =
Wavelength * Frequency, or v = f * 
Wind instruments use this concept of sound
waves, or standing waves when air is created inside of them. A
sound wave is introduced into a medium, in this case, air, through a vibrating
object. The air particles move back and forth because of the vibrating object.
When the particles vibrate, they cause other particles near them to vibrate at
the same frequency. A vibration made
at the mouthpiece of an instrument is picked up and amplified by the air inside
of the tube-shaped body of the instrument. Sound is produced when waves of
specific lengths are trapped in the instrument. The pitches of the sound waves
are created by the dimensions of the tube. The note is heard when the waves
exit the end or ends of the tubes. In a tube with both ends open, like a
xylophone, the lowest note possible, the fundamental, has a wavelength twice
the length of the tube. The next note has twice the frequency or wavelength of
the fundamental, the next three times the frequency, and so on.
Allowed Waves in an Open Tube
In
a tube with only one open end, like a saxophone, the fundamental has a
wavelength four times the length of the tube. The next possible note has three
times the frequency of the fundamental, the next five times, and so on.
Allowed
Waves in a Half-Open Tube
We
are able to use the information above to calculate the lengths of each tube.
The length of each tube affects the wavelength, and therefore, affects the
pitch. The lengths of the pipes can be found
by using the formula
Length=
speed of sound
Frequency
Here
is an example. If we want to make the note “A”, we take the speed of sound, roughly
343.8 meters per second, divided by the frequency of the note, 440 Hertz. One
Hertz equals one vibration/second. The resulting length is 78.136 centimeters.
However, this is not the exact length. To account for the two open ends of the
tube, we need to take 2 times the radius, ¾ of an inch, and subtract it from
the previous amount. This puts the tube at about 74.326 centimeters long. We
can repeat the process with the different frequencies to find all of the
lengths we will need.
Sound
waves can be applied to the way wind instruments function. By using wave
patterns, frequencies, and the speed of sound, we are able to calculate the
proper length for each tube. Technically, our xylophone will be a wind
instrument because we are pushing air through the tubes to make sound. It is
also a percussion instrument because you hit it with paddles to play it.
Bibliography
Cnx.org.
Physicsclassroom.com. 2004.
<http://www.physicsclassroom.com/Class/sound/soundtoc.html>.
Grc.nasa.gov. First Gov. 15 Dec. 2006 <http://www.grc.nasa.gov/WWW/K-12/airplane/andwave.html>.
Kettering.edu. 2002.
|
Exploratorium Home |