Wave Power & Energy Calculator (String)
Find the average power a transverse wave carries along a string, plus its energy per period and per wavelength.
How it works
P = ½ · μ · ω² · A² · v · with ω = 2π·f · Energy per period = P ÷ f
A transverse wave on a string transports energy without moving the string along, at an average power P = ½μω²A²v. The power scales with the square of both the amplitude and the frequency, so doubling the amplitude or the frequency quadruples the power delivered. Denser strings and faster waves also carry more power, which is why the energy in a wave depends so strongly on how vigorously and how quickly it is driven.
Worked example
A string with μ = 0.01 kg/m carries a wave of amplitude 0.02 m at 50 Hz travelling at 30 m/s. ω = 2π × 50 ≈ 314.2 rad/s, so P = ½ × 0.01 × 314.2² × 0.02² × 30 = ½ × 0.01 × 98,696 × 0.0004 × 30 ≈ 5.92 W. Each period carries 5.92/50 ≈ 0.118 J.
Sources: Wave power (physics) — Wikipedia
Frequently asked questions
Why does amplitude matter so much?
Power depends on amplitude squared, so a wave with twice the amplitude carries four times the power. The same square-law applies to frequency, making high-amplitude, high-frequency waves far more energetic.
Does the wave move the string down the line?
No — the string particles oscillate in place while energy travels along. The wave transports energy and momentum, not the material of the string itself.
How do I get the wave speed?
For a string it is v = √(T/μ), the square root of tension divided by linear density. A tighter or lighter string carries waves faster; enter that speed here.
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This calculator is for educational purposes. Double-check important results before acting on them.