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Energy transport in waves
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Power carried by a string wave.
P = ½μω²A²vA sinusoidal wave on a string carries average power P = ½μω²A²v: proportional to the square of both amplitude and frequency.
Doubling frequency at fixed amplitude gives four times the power.
Energy flows in the direction of propagation.
In more detail
Waves transfer energy, with the average power proportional to the square of amplitude and frequency. The energy moves with the group velocity, not necessarily with the wave crests.
Real-world uses
- Ocean waves carry energy to shores where it can be harvested.
- Seismic waves carry energy from earthquakes across the globe.
- Engineers calculating the power delivered by a vibrating string use the wave energy transported along it.
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Frequently asked questions
Does the wave carry matter?
No. It carries energy, while the medium only moves locally.
How does energy depend on amplitude?
It is proportional to the square of amplitude.
Does power depend on the amplitude?
Yes. The power is proportional to the square of the amplitude, so doubling the amplitude gives four times the power.
Related topics in Waves & Sound
Doppler in light · Shock waves and sonic boom · Mach number · Wave packets and group velocity · Dispersion · Waves in water