Lesson 3 · 14 min
Superposition and standing waves
Linear media add. Boundaries pick the wavelengths that fit. That is a guitar, an organ, and an AC line.
Fit the boundary
Two waves of equal frequency traveling opposite ways make a standing wave: nodes that never move, antinodes that move a lot. A string fixed at both ends must have nodes there, so L = n λ/2, n = 1, 2, 3… The frequencies are then nf₁, a harmonic series. That is why a guitar string sounds like a note and not like noise.
f_n = n v / (2L) n = 1, 2, 3, …
Fundamental n = 1. A pipe closed at one end uses odd harmonics: L = nλ/4 with n odd.
Check
The second harmonic on a 0.80 m fixed string with v = 240 m/s has frequency