Interference
Author: Lenore Horner

The red wave is the superposition (sum at every point and every time) of the black and the blue waves. Assume the two sounds come from two different speakers.  The red wave is then what a listener at various distances from the speakers (various positions on the horizontal axis) hears.

When the φ values are both at 0, both speakers are located at the origin.  Changing the φ values corresponds to changing the positions of the speakers.  Note what listeners standing at different distances from the speakers (different positions on the horizontal axis of the graph) here.

sound 1

sound 2

total sound - superposition of sounds 1 & 2

a_1 = 1 (slider from -5 to 5, step 0.1)
ω_1 = 50 (slider from -5 to 50, step 0.1)
φ_1 = 0 (slider from -5 to 5, step 0.1)
f(x) = a_1 * sin(ω_1 * x + φ_1)
a_2 = 1 (slider from -5 to 5, step 0.1)
ω_2 = 50 (slider from -5 to 50, step 0.1)
φ_2 = 0 (slider from -5 to 5, step 0.1)
g(x) = a_2 * sin(ω_2 * x + φ_2)
h(x) = f(x) + g(x)