Formula describing starting wave, plus 2N reflections:
Check on the formulas above by animating starting wave (at top of plot) and subsequent reflections (as move downward in plot). As one wave strikes the wall of the box, the amplitude of reflected wave (next lower in plot) should match at wall:
Animation of the cumulative wave in a 5 cm long box (starting wave plus 50 reflections). As the animation progresses, the wavelength of the wave is gradually increased from ~ 0 cm to 10 cm.
Note the wavelengths at which strong peaks occur:
1.25 cm, 1.66 cm, 2.5 cm, 3.33 cm, 5 cm, 10 cm = L/4, L/3, L/2, 2L/3, L, 2L
These are the wavelengths that fit in the box. Or more accurately, it is when an integral number of lambdas fit into twice the box's length (up and back): n lambda = 2 L, or
lambda = 2L / n.
These are called "standing waves" because, while they still oscillate up and down, they "stand" in the sense that they do not move left or right:
Other Materials Relevant to the Lecture:
YouTube Videos on "Reuben's Tube" flame demonstrations of standing waves:
Video of salt patterns generated by standing waves on a sound stimulated square plate: