Category: 09 Waves

905 Phase Relationship

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. A quarter-cycle coreesponds to 90° or π/2 rad. So on and forth.

These four oscillations are in-phase with one another (phase difference of 0, 2π, 4 π, …)

The 1st and the 3rd are complete out-of-phase (phase difference of π, 3π, 5 π, …) with the 2nd and the 4th.

Each oscillation lags the one on the left a quarter-cycle (π/2 rad).

Each oscillation lags the one on the left 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.

904 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

903 Wave Speed

Wave crest advances by one wavelength every one period

In the same medium, wave speed is constant. A wave half the wavelength has twice the frequency.

Wave speed is different in different medium. For the same frequency, the wave with longer wavelength propagates at a faster speed.

🍏 <phet applet>

 

900 Wave

Water wave is an example of a 2D wave that propagates along a surface.

Notice the bob does not travel with the wave.

Each medium particle oscillate about its own equilibrium position. Their oscillatory motion result in the propagation of the energy/momentum.

Is sound a wave or a stream of particles?