Download 3-D Standing Wave Machine

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3-D Standing Wave
Machine
P6-7800
BACKGROUND:
A wave is a disturbance that travels through a material, often referred to as a medium. Waves 1)
transmit energy without transporting mass; 2) are characterized by their amplitude, frequency and
wavelength; and 3) pass through one another and come out unchanged. When waves occupy the
same space at the same time, they combine to form a single resultant wave. This phenomenon,
which is unique to waves, is called interference.
Nature uses simple algebra when dealing with overlapping waves. When two waves meet, the
medium through which the waves are traveling will take on a height, or amplitude, that is the
algebraic sum of the amplitudes of the two waves. For example, if both waves are crests and one
wave has an amplitude of +2 units and the other wave has an amplitude of +3 units, the amplitude
of the superimposed waves will be +5. Similarly, if one wave is a crest with an amplitude of +5 and
the other wave is a trough with an amplitude of -2, the resultant amplitude will be +3. If the
amplitudes of the two waves are +3 and -3 respectively, the waves will cancel out completely.
A fixed pattern, called a standing wave, may be produced when two identical trains of waves move in
opposite directions through the same medium. For example, standing waves may be set up quite
easily by disturbing both ends of a string. In some regions, the two waves add together to make a
larger wave (constructive interference). In other regions the waves cancel each other out and the
string moves very little, if at all (destructive interference). The regions where the motion of the string
is most pronounced are called antinodes. The regions where string is at rest are called nodes. It
should be noted that standing waves will occur for only certain values of the wave frequency and
string length.
In a standing wave, the distance between adjacent nodes, or between adjacent antinodes, is equal
to one-half wavelength. The number of antinodes determines the harmonic of the standing wave. As
the term harmonic may suggest, standing waves are the basis for the sounds produced by many
musical instruments. Standing waves are also responsible for the production of light by gas lasers.
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ANN ARBOR, MI 48106 T 800-367-6695
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©2009 ARBOR SCIENTIFIC ALL RIGHTS RESERVED
At the heart of the 3-D Standing Wave Machine is a string attached to the shafts of two small,
variable speed motors. Each motor sends out a continuous train of waves that travel along the string.
These waves interfere to form standing waves.
ACTIVITIES:
1. The wave machine may be used in a physics, physical science, or mathematics classroom as
a demonstration device or as a station in an exploratory laboratory on waves. The wave
machine is certain to draw a crowd if used in a hallway display case. When operating in its
“demo” mode, the device produces an amazing array of constantly changing standing and
traveling wave patterns. Your own DC power supply (6 Volts, 1 Amp) can be used which
eliminates the need for batteries and allows continuous operation of the wave machine.
2. Characteristics common to all waves (amplitude, wavelength, and period) may be easily
demonstrated. The novelty of this unique wave generator enhances both understanding of
and interest in wave phenomena.
3. The conditions required for the production of standing waves can be shown by changing the
tension in the string and the frequency of the motors. Students will see that only certain
combinations of tensions and frequencies give rise to standing waves.
4. The LEDs may be used to illustrate color mixing. Since the colors projected on the string may
be controlled, color addition may be easily demonstrated. For example, it may be shown that
red + blue = magenta, red + green = yellow, green + blue = cyan, and that red + blue + green
= white.
5. The flashing LEDs may be used to introduce the concept of persistence of vision, the
eye/brain’s ability to retain an image for a short period after a source of light is turned off. By
adjusting the flash speed and pulse control, students can “freeze” the motion of the string or
produce what appear to be multiple strings.
6. The wave machine is the perfect adjunct to a mathematics lesson on the addition of curves.
After students are introduced to the mathematical addition of curves, they can see how
nature approaches the problem.
RELATED PRODUCTS:
Standing Wave Kit 10 Pack (P6-7700) provides students with an introduction to standing waves.
The Light Box & Optical Set (P2-9561) allows students to perform hands on color mixing.
BIBLIOGRAPHY:
Conceptual Physics: The High School Physics Program. Paul G. Hewitt. Pearson Education, Inc.
PO Box 2750
ANN ARBOR, MI 48106 T 800-367-6695
WWW.ARBORSCI.COM
©2009 ARBOR SCIENTIFIC ALL RIGHTS RESERVED