Standing Waves on a String

Change the harmonic number and observe how nodes, antinodes, wavelength, and frequency change on a string fixed at both ends.

Harmonicn = 1

Wavelength, λₙ4.00 m

Frequency, fₙ10.00 Hz

Nodes2

Antinodes1

Parameters

Harmonic number, n 1

n = 1 is the fundamental; n = 2, 3, … are higher harmonics.

Amplitude, A 1.00 m

Maximum displacement at an antinode.

String length, L 2.00 m

The ends remain fixed at x = 0 and x = L.

Wave speed, v 20.0 m/s

For a given string, v determines the harmonic frequencies.

y(x,t) = A sin(nπx/L) cos(2πfₙt), λₙ = 2L/n, fₙ = nv/(2L)

Fundamental mode: There are two fixed nodes at the ends and one antinode at the center.

string at current time nodes antinodes maximum envelope

Predict before moving the harmonic slider

Change from n = 1 to n = 2. What happens to the number of antinodes, wavelength, and frequency?