University Physics I - Classical Mechanics, 2019

12.3. CONCLUSION, AND FURTHER RESOURCES 293
12.3 Conclusion, and further resources
This chapter on one-dimensional waves has barely scratched the surface of the extremely rich world
of wave phenomena. I have only given you a passing glance at interference, and I have not said
anything at all about diffraction, the Doppler effect, polarization, refraction.... Many of these
things you will learn about in later courses, most likely when you encounter electromagnetic waves
(which are non-mechanical, but described by the same mathematical equation).
Waves are such an intrinsically kinetic phenomenon that they are best appreciated by watching
them in action, or, as a second-best alternative, through animations. A wonderful repository
of such movies and animations is PHYSCLIPS at the University of New South Wales:
http://www.animations.physics.unsw.edu.au/waves-sound/oscillations/index.html
They also have a set of pages on the “physics of music” that I have already mentioned a couple of
times. If you are interested in this topic, you should go spend some time there!
http://newt.phys.unsw.edu.au/music
Finally, closer to home, the fellows at PhET (University of Colorado), have this great interactive
apptoexplorewavesonastring:
https://phet.colorado.edu/en/simulation/wave-on-a-string
12.4 In summary
1. A traveling wave in an elastic medium is a collective disturbance of the particles in the medium
(a displacement, or change in pressure or density) that carries energy and momentum from
one point of the medium to another, over a distance that is typically much larger than the
displacement of the individual particles making up the wave.
2. In a longitudinal wave, the displacement of the particles is along the line of motion of the
wave; in a transverse wave, it is perpendicular to the wave’s motion.
3. An important kind of waves are periodic waves, in which the disturbance repeats itself at
each point in the medium with a period T . Sinusoidal, periodic waves are called harmonic
waves. Their spatial period is called the wavelength λ. If the speed of the wave is c, one has
c = fλ,wheref =1/T is the wave frequency.
4. The time-averaged energy density in a harmonic wave (sum of kinetic and elastic potential
energy per unit volume) is E/V = ρ 0 ω 2 ξ 2 0 /2, where ρ 0 is the medium’s density, and ξ 0 the
amplitude of the displacement oscillations. The time average momentum density is E/cV .
The intensity of the wave (energy carried per unit time per unit area) is cE/V .