When two sine waves are superimposed, the resulting wave is a combination of the individual waves. The amplitude of the superposition wave depends on the relative phase and amplitude of the component sine waves.
Let's consider two sine waves with the same frequency, but different amplitudes and phases. The first sine wave can be represented as A1sin(wt + φ1), where A1 is the amplitude and φ1 is the phase. The second sine wave can be represented as A2sin(wt + φ2), where A2 is the amplitude and φ2 is the phase.
When these two sine waves are superimposed, the resulting wave is the sum of the individual waves at each point in time. Mathematically, the superposition wave is given by:
Superposition = A1sin(wt + φ1) + A2sin(wt + φ2)
The amplitude of the superposition wave is determined by the maximum value of this combined wave. To find the maximum amplitude, you can use trigonometric identities or techniques like vector addition.
If the phases of the two waves are the same (φ1 = φ2), the amplitude of the superposition wave is the sum of the individual amplitudes: Amplitude_superposition = A1 + A2.
If the phases of the two waves are opposite (φ1 = -φ2), the amplitude of the superposition wave is the difference of the individual amplitudes: Amplitude_superposition = |A1 - A2|.
In other cases where the phases are different and not in these specific conditions, determining the exact amplitude of the superposition wave requires analyzing the specific values of the amplitudes and phases involved in the wave equation.
It's important to note that superposition can also result in destructive interference, where the amplitude of the combined wave may be smaller than the individual amplitudes, or complete cancellation, where the amplitude becomes zero. The exact outcome depends on the specific values of the amplitudes, phases, and frequencies involved in the superposition.