Wave Speed on a String

Wave speed on a stretched string: v = √(T/μ), where T = tension (N), μ = mass per unit length (kg/m).

Depends ONLY on the medium (string), not on the frequency or amplitude.

Increasing tension ⇒ faster wave. Increasing μ (heavier string) ⇒ slower wave.

Wavelength λ adjusts to keep v = fλ correct in each medium.

Pluck a guitar string: travel up and back to form a standing wave; tuning is done by adjusting T (peg) or μ (different strings).

Two strings with same T but different μ have different speeds — basis of musical-instrument variety.

Power transmitted by a sinusoidal wave: P = ½μω²A²v.

If string crosses a boundary (e.g., light to heavy section), partial reflection + transmission occur.