← Oscillations and wave anatomy

Amplitude carries the energy

Two beach days, same long swell lines, same spacing between them. On the calm day the waves patter against the breakwater. On the storm day, crests twice as tall ride in, and each one slams it.

Same wavelength, same speed, same rhythm; only the height changed, and the hits got harder. That is a claim about energy, and this lesson pins it down.

Hold everything else constant and change only the amplitude: same medium, same wavelength, same speed.

rest positionrest positionsmall amplitudelarge amplitudeequal crest spacing in both
Only the amplitude differs between the two waves: same spacing, same speed, different swing.

A larger amplitude means the medium's particles swing farther from their rest positions as the wave passes.

Swinging farther takes more energy, so a larger-amplitude wave carries more energy.

Ripples with taller crests hit the shore harder: the energy arriving at the shore each second is greater.

Turn it down and it runs the other way: a smaller amplitude means smaller swings and less energy carried.

The direction of the changeamplitudeparticle swingsenergy carriedlargerfarther from restmoresmallerless far from restless
Amplitude up, energy up; amplitude down, energy down. Everything else held constant.

So amplitude is the size number that carries the energy story: taller crests, more energy; lower crests, less.

How MUCH more is beyond this course's depth: the direction of the change is the claim here.

Beata's wave tank paddle swings at one steady rate, first through a small arc, then through a large arc. The floats at the far end barely stir, then jump. Why?

The larger arc makes waves with a larger amplitude, everything else unchanged.

A larger amplitude means the water's particles swing farther, so the waves carry more energy.

More energy arrives at the floats each second.

The large-arc waves carry more energy, so the floats jump.

Anselm sends waves along a rope to a ribbon at the far end, then sends smaller swings at the same rate. What happens to the energy arriving at the ribbon, and what shows it?

Smaller swings mean a smaller amplitude, everything else unchanged.

A smaller amplitude means the rope's particles swing less far, so the waves carry less energy.

Less energy arrives at the ribbon each second; the ribbon barely flicks.

Ripples from Anselm's paddle rise 2 cm above rest; ripples from Beata's paddle on the same pond rise 6 cm, with matching wavelength and speed. Whose ripples carry more energy?

A wave machine's crests are raised to three times their height, with the medium, wavelength, and speed unchanged. What happens to the energy the waves carry?

Dilys says: 'A rope wave with smaller swings carries less energy along the rope, everything else equal.' Is Dilys correct?

Your turn

Four settings of one wave tank keep the same medium, wavelength, and speed. Which setting makes the waves carry the most energy?

Why does a larger-amplitude wave on a rope carry more energy, everything else equal?

At a breakwater, winter swells arrive with crests 3 m above rest; summer swells arrive with crests 0.5 m above rest, with matching wavelength and speed. Which statement is correct?