gen-in-3-4-sentences-explain-standing-waves-on-a-string-state-an-526c

In 3-4 sentences, explain standing waves on a string. State any key formula.

Standing waves form on a string when two waves of equal frequency and amplitude traveling in opposite directions interfere with each other, creating points of zero displacement (nodes) and maximum displacement (antinodes) that remain stationary. These waves only occur at specific resonant frequencies determined by the string's length, tension, and mass density. The key formula for the allowed wavelengths is: **λₙ = 2L/n**, where L is the string length and n = 1, 2, 3, ... is the harmonic number. The corresponding frequencies are **fₙ = nv/2L**, where v = √(T/μ) is the wave speed (T is tension, μ is linear mass density).