Meteorological Instrument Performance Characteristics

Dynamic Response » Response to Specific Input Functions » Superposition Illustration

Explore the following animations, which illustrate the Principle of Superposition. (For more details, see the Superposition of Waves page created by Daniel A. Russell at The Pennsylvania Sate University,

Opposite Pulses

Superposition of two opposition direction wave pulses. The animation shows two Gaussian wave pulses are travelling in the same medium but in opposite directions. The two waves pass through each other without being disturbed, and the net displacement is the sum of the two individual displacements.


Two waves (with the same amplitude, frequency, and wavelength) are travelling in the same direction. Using the principle of superposition, the resulting wave displacement is a travelling wave whose amplitude depends on the phase (ϕ). When the two waves are in-phase, they interfere constructively and the result has twice the amplitude of the individual waves. When the two waves have opposite-phase, they interfere destructively and cancel each other out.

Opposite Sine Waves

A travelling wave moves from one place to another, whereas a standing wave appears to stand still, vibrating in place. In this animation, two waves (with the same amplitude, frequency, and wavelength) are travelling in opposite directions. This wave is no longer a travelling wave because the position and time dependence have been separated.

Different Frequencies

Two waves of equal amplitude are travelling in the same direction. The two waves have different frequencies and wavelengths, but they both travel with the same wave speed. The resulting particle motion is the product of two travelling waves. One part is a sine wave which oscillates with the average frequency, which is the frequency perceived by a listener. The other part is a cosine wave.