Imagine two identical waves with equal amplitudes, but they are out of phase with each other. To illustrate this, let's consider the example of two simple harmonic waves, represented by the equations:
Wave 1: y1(t) = A * sin(ωt)
Wave 2: y2(t) = A * sin(ωt + φ)
In these equations:
- A is the amplitude of the waves (the maximum displacement from the equilibrium position).
- ω is the angular frequency of the waves (determines how fast the wave oscillates).
- t is time.
- φ is the phase difference between the two waves.
Both waves have the same amplitude (A) but differ in phase (φ).
For instance, let's say Wave 1 and Wave 2 are both sine waves with an amplitude of 1 unit and an angular frequency of 2π radians per second. However, Wave 2 is shifted by a phase difference of π/2 (90 degrees) compared to Wave 1.
Wave 1: y1(t) = sin(2πt)
Wave 2: y2(t) = sin(2πt + π/2)
If you plot these waves, you will see that they have the same amplitude (both oscillate between -1 and +1) but have different starting points and positions throughout time due to the phase difference:
sql