Question

How do you find the resultant amplitude when two waves have different amplitudes and different phases (or vice versa)?

Answer 1

To find the resultant amplitude of two waves with different amplitudes and different phases, you can use vector addition. The process involves considering the waves as vectors in the complex plane and adding them together. The complex representation allows us to handle both the amplitude and phase of the waves simultaneously.

Let's consider two waves with different amplitudes and phases represented as:

Wave 1: $A_1$ (amplitude) and ${\varphi }_1$ (phase) Wave 2: $A_2$ (amplitude) and ${\varphi }_2$ (phase)

The complex representation of each wave can be expressed as:

Wave 1: $A_1\cdot e^{i{\varphi }_1}$ Wave 2: $A_2\cdot e^{i{\varphi }_2}$

where $i$ is the imaginary unit ($i^2=-1$), and $e$ is Euler's number.

Now, to find the resultant amplitude, you need to add these complex representations together:

Resultant Amplitude = Aresultant=A1⋅eiϕ1+A2⋅eiϕ2A_{ ext{resultant}} = A_1 cdot e^{i phi_1} + A_2 cdot e^{i phi_2}<span class="kate