This note describes how to demonstrate traveling wave patterns, as opposed to standing wave patterns, with sets of uncoupled pendula using an apparatus known as Mach's wave machine. Both transverse and longitudinal variants of the wave machine are discussed, as are ways to independently adjust wave speed, amplitude, and frequency (and hence wavelength) of the traveling wave patterns.
REFERENCES
1.
W. Weiler, Physikbuch #3: Schwingungen und Wellen, (J.F. Schreiber, Esslingen, and Munchen, 1910), pp. 6–7.
2.
These are not actual traveling waves in a technical sense because the pendula are uncoupled, so information is not transmitted from one oscillator to the next. Hence we call them traveling wave patterns instead.
3.
An even more classic simple harmonic oscillator is the mass-on-a-spring. One could build a transverse Mach's wave machine using a set of identical mass/spring oscillators hanging side by side from a horizontal beam, lifting them together to cock the apparatus, then releasing them one by one. A longitudinal wave machine based on masses and springs is somewhat harder to envision, since vertical springs would tend to interfere with the normally vertical motion of the oscillating masses. One possible design might use a set of masses in a vertical line, each of which is supported from the side by two or more horizontal springs.
4.
R. E.
Berg
, “Pendulum waves: A demonstration of wave motion using pendula
,” Am. J. Phys.
59
(2
), 186
–187
(Feb. 1991
).5.
J. A.
Flaten
and K. A.
Parendo
, “Pendulum waves: A lesson in aliasing
,” Am. J. Phys.
69
(7
), 778
-782
(July 2001
).
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© 2005 American Association of Physics Teachers.
2005
American Association of Physics Teachers
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