Medium sets speed, source sets frequency

Griet shakes the end of a long rope, sending a steady train of waves toward a post. Then she doubles her shaking rate.

Waves now leave her hand twice as often. Do they cross the rope any faster?

No. The crests leave more often, but each crest crosses the rope in the same time as before.

Slow shaking: the train's front reaches 6 m at t = 2 s.

Fast shaking: more crests, and the front still reaches 6 m at t = 2 s.

What the source does sets the frequency. Shake faster, and more waves leave each second: the frequency rises.

What the medium is sets the speed. The rope itself decides how fast any crest can travel along it: how heavy the rope is, and how tightly it is stretched.

Once a wave has left the source, the source cannot reach it again. The wave keeps the frequency it was made with all the way down the rope because wave speed is set by the properties of the medium, while frequency is set by the vibrating source and does not change as the wave travels.

So the jobs divide cleanly. The source owns the frequency. The medium owns the speed.

The division of labor.

To change a wave's speed, change the medium: a different rope, or deeper or shallower water. Shaking faster never does it, and shaking harder never does it either.

Eirik doubles the rate at which he shakes the end of a long spring. What happens to the frequency and the speed of the waves on the spring?

The source now vibrates twice as often, so the frequency doubles.

The spring itself is unchanged, so the wave speed stays the same.

The frequency doubles; the speed does not change.

One wave machine, on one setting, sends waves first along a light cord and then along a heavy rope. What is the same about the two waves, and what differs?

The source vibrates the same way both times, so both waves have the same frequency.

The two mediums differ, so the two wave speeds differ.

Same frequency, because the source is the same; different speeds, because the mediums differ.

A pulse travels along a stretched cord. What decides the pulse's speed?

Waves travel along a rope toward a post. What decides their frequency?

Fenna says: 'Shaking the end of a rope faster makes more waves each second, but it does not make them travel faster.' Is Fenna correct?

Your turn

Hale cranks a wave machine's paddle faster in a tank of water. Which quantity rises?

A paddle makes water waves at 3 Hz at one end of a long tank. The waves travel to the far end. What is their frequency near the far end?

Eirik wants the waves on his rope to travel faster. Which change works?