Wave Interference & Superposition Physics

Beat frequency: --- Hz

Wave 1

1.00
2.0
0.00

Wave 2

0.80
2.2
0.00
0.00

What is Wave Interference & Superposition?

Quick Answer: This interactive tool plots two traveling waves (sine, square, triangle) and their sum. Adjust amplitude, frequency, phase, and watch the resultant wave. When frequencies are close, beats appear. It illustrates the principle of superposition: the net displacement is the algebraic sum of individual displacements.

Theory of Superposition and Beats

According to the principle of superposition, when two or more waves overlap, the resultant displacement at any point is the sum of the individual displacements. For two waves y1(x,t) = A1 sin(k1x - ω1t + φ1) and y2(x,t) = A2 sin(k2x - ω2t + φ2), the resultant is y = y1 + y2. When frequencies are slightly different, the amplitude of the resultant varies periodically, producing beats. The beat frequency is fbeat = |f1 - f2|. The simulation assumes waves travel with speed v = 1 unit/s (so k = ω). You can pause the animation and explore any instant.

Step-by-Step Examples

Example 1: Constructive and Destructive Interference

  1. Set both waves to sine, equal amplitude (1.0) and frequency (2 Hz), zero phase. The resultant is a sine wave with double amplitude (constructive everywhere).
  2. Change phase of wave 2 to π (3.14). The waves cancel completely – destructive interference.

Example 2: Beats

  1. Set f1 = 2.0 Hz, f2 = 2.2 Hz. Observe the resultant wave's envelope modulation over time. Drag the time slider or press Animate to see the amplitude wax and wane. The beat frequency is 0.2 Hz.

Example 3: Different Wave Shapes

  1. Choose square wave for wave 1 and triangle for wave 2. Notice the complex resultant. The superposition still holds algebraically.

Frequently Asked Questions

How is wave speed determined?

For simplicity, the wave speed is set to 1 unit/s. Thus wavenumber k = 2πf (since v = fλ = 1). You can adjust only frequency; k is linked.

What does the time slider do?

It advances the wave phase (ωt). You can manually scrub time or click Animate to auto-play.

Why do beats occur?

When two waves have close frequencies, their superposition results in a wave whose amplitude varies at the difference frequency (|f1 - f2|).

Can I see standing waves?

Standing waves form when two identical waves travel in opposite directions. This simulation currently shows waves traveling in the same direction. To see standing waves, set equal frequencies and amplitudes, then flip the sign of k (not implemented).

Are non-sinusoidal waves accurately represented?

Square and triangle waves are generated as mathematical functions (sign of sine, linear ramp). They are ideal and may have infinite bandwidth conceptually, but the plot is accurate to the formula.