Saturday, July 14, 2012

Traveling & Standing Waves in Water

Traveling Waves

I recall jerking a garden hose, then seeing the bend I'd made travel away from me down a finite length of the hose. This retreating bend, or pulse, is a traveling wave.

Waves are caused by a disturbance - an input of energy - that travels through spacetime while the energy of the disturbance is transferred and dissipated.

A traveling wave is seen when the wave is not confined to a given space along the medium such as ocean waves approaching a shoreline.
The sea pronounces something, over and over, in a hoarse whisper; I cannot quite make it out.
~Annie Dillard
Ocean waves can travel thousands of miles before reaching land.

From the Wave

It mounts at sea, a concave wall
   Down-ribbed with shine,
And pushes forward, building tall
   Its steep incline.

...opening stanza from a poem by Thom Gunn

Standing Waves

A standing wave is stationary. It is confined in some way by natural or man-made contraints.

A vibrating guitar string is an example of a standing wave. A guitar string has a number of frequencies at which it will vibrate (i.e., the harmonics of the guitar string). The frequency at which a guitar string vibrates depends on the tension of the string, the linear density of the string and its length.

Standing Waves in Rivers

Standing waves in rivers are caused by a high volume of water constricted by flowing into and over a structure like a submerged boulder and creating a wave behind it known as a hydraulic jump. Thought another way, when flowing water encounters a zone of slower moving water a abrupt rise occurs in the surface of the water.

Standing waves can been ridden like the river surfers on the Eisbach in Munich (below). The Eisbach river surfers catch the wave by launching into it from the sides, then facing upstream while traversing its stationary wave front.

The Eisbach wave is about 3' high. Enthusiasts have modified the wave to boost its height and to break more cleanly by submerging planks attached to an upstream bridge.

Surfing a standing wave gives the sensation of traveling over water while not actually moving. A standing wave can be surfed for as long as one maintains the right position and balance.
How could drops of water know themselves to be a river? Yet the river flows on.
~Antoine de Saint-Exupery

Further Reading