Wave Speed on a String
v = √(T/μ).
Key Notes
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.
Formulas
Wave-speed on string
T in newtons, μ in kg/m, v in m/s.
Mass per unit length
Total mass / length; for a uniform cross-section.
Power transmitted
Quadratic in both A and ω.
Tension changes speed
Useful for comparison in same string.
Important Points
v on string depends only on T and μ. Independent of f and A.
To tune a guitar string UP in pitch: tighten (increase T) ⇒ faster wave ⇒ shorter wavelength fits the fundamental ⇒ higher f.
Thicker (heavier) strings give LOWER notes — at same T, larger μ ⇒ slower v ⇒ lower f.
Power transmission scales as A² and ω².
If a string is stretched 4× (T ×4), wave speed doubles.
Real strings have stiffness — harmonics deviate slightly from ideal (inharmonicity).
Wave Speed on a String notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.