Category: 09 Waves

132 Human Wave

We can apply the concept of phase to any repetitive periodic motion. One complete cycle corresponds to 360° or 2π rad. Half-a-cycle corresponds to 180° or π rad. One and a quarter-cycle coreesponds to 450° or 5π/4 rad. So on and forth.

See if you can recognize the phase differences among the following oscillations.

In-phase (phase difference of 0, 2π, 4 π, …)

Complete Out-of-Phase (phase difference of π, 3π, 5 π, …)

Quarter-cycle Phase Difference (Each oscillation leads the one on the right by π/2 rad)

Each oscillation leads the one on the right by 1/8 of a cycle (45° or π/4 rad). The profiles of two progressive waves moving from left to right are now clearly visible. There is the transverse wave in the bobbing heads, and the longitudinal wave in the gyrating hips. 😛

In an actual progressive wave, there is a continuous increasing phase lag in the direction of wave propagation. Each wave element lags the preceding wave element by a bit.

119 Slinky Drop

The monkey hovers in the air because its weight is balanced by the tension force of the slinky. It remains hovering as long as the bottom end of the slinky continues to be stretched by the same amount. From simple mechanics we can understand why the monkey does not drop immeditely, because it takes time before the unstretching progresses down the slinky. However, why must the entire slinky collapse before the bottom end starts to unstretch?

The above video shows that when a rubber band is used instead, it still takes sometime before the bottom end starts to unstretch. However, unlike the slinky, there is no need for the entire rubber band to collapse before the bottom end starts to unstretch. So what’s so special about the slinky?

I was about to delete the above video when I noticed something interesting. By accident, a longitudinal compression wave was sent down the slinky just before it was dropped. So this video captured two “things” racing down the slinky. There is an ordinary longitudinal compression wave that travels at a speed as dictated by the mass and tension of the slinky. Hot on its heels is the collapsed slinky. The video shows quite clearly that the collapsed slinky actually travels faster than an ordinary compression wave would down the slinky. The “collapse”, being accelerated by both gravity and the tension force of the slinky below it, pushes into the slinky faster than a compression wave can propagate down the slinky.

That explains why the monkey does not drop before the slinky collapses totally. The medium itself (the slinky) travels faster than the wave. The entire slinky collapses before the disturbance can reach the monkey.

Learn more about shockwave

Wave Crank — xmdemo 082

A transverse wave (the green one) is one in which the oscillations are perpendicular to the direction of wave propagation.

A longitudinal wave (the red one) is one in which the oscillations are parallel to the direction of wave propagation. It is interesting that a longitudinal wave sets up regions of compression and rarefaction. Notice also that the compression and rarefaction always occur at the point which is at its equilibrium position.


074 Polarization by Reflection

When light passes from air to glass, some of it is refracted into the glass, and some of it is reflected. The reflected light is partially polarised because light polarised horizontally is reflected more strongly than light polarised vertically. In fact, at one particular angle of incidence called the Brewster’s angle, light polarised horizontally is 100% refracted, resulting in a 100% vertically polarised reflected light.

This phenomenon occurs for any transparent material, including glass, paint and water.

Further reading:

069 Polarised and Unpolarised Light

If light passing through ONE single polarizer shows variation in brightness as the polarizer is rotated, it must mean that the light is polarized.

As shown in the video, filament lamps, fluorescent lamps and the Sun emit light that is unpolarised.

The display screens of calculators, handphones and LED TV are all based on LCD (Liquid Crystal Display) technology, which produces polarized light.

055 When Newton Meets Einstein

The picture of Newton was in green only, while the picture of Einstein was in red color only. Green and red light from the LCD projector are polarised perpendicularly with each other. As polarizer was rotated, it cut off either the green or the red so that only either Newton or Einstein comes into view.

Some 3D movies are made this way. The image meant for the left and right eyes are projected using two mutually perpendicular polarised light. The viewers are then given glasses which are fited with polarizers.


053 Polarisation (Three Polarizers)


After polarizer 1, the light polarized at 0° with amplitude E0 and intensity I0.

After polarizer 2, the light becomes polarized at 45°, and its amplitude is reduced to E0cos45° and intensity 0.5I0

After polarizer 3, the light becomes polarized at 90°, and its amplitude is reduced to (E0cos45°) cos45°=0.5E0 and intensity 0.25I0

By inserting polarizer 2, no two consecutive polarizers are perpendicular, and the light is never completely wiped out at any stage.

052 Polarisation (Two Polarisers)

EM wave

A light wave has E-field oscillating at right angle to its direction of propagation. A polarizer allows only the component of E-field in the polarizer’s orientation to pass through.


So the first polarizer polarizes the unpolarized light. Because an unpolarized light has light in all orientations, its intensity always drops to half after passing through the first polarizer, regardless of how the polarizer is oriented.

If the second polarizer is oriented at the same angle as the first, then 100% of the polarized light is passed through. If the second polarizer is perpendicular to the first, then 0% of the polarized light is passed through. If the second polarizer is misaligned with the first by an angle θ, the amplitude of the polarized light will drop from E0 to E0cosθ, and the intensity will drop from I0 to I0cos2θ.