Question

7. Find the resultant of the superposition of two harmonic waves in the form: E = E0 sin(ωt +α) with amplitudes of 3 and 4 and phases of 30° and 90°, respectively. Both waves have a period of 1 s.

Answer 1

Use Phasor diagram for this.

The wave with amplitude 3 units and phase of 30 degrees will be represented 30 degrees above the positive x axis and the wave with amplitude 4 units and phase 90 degrees will be along positive y axis.

Then net electric field along x axis will be:

E_x = 3cos30 + 0 = 2.598 units

and along y axis: E_y = 3sin30 + 4 = 5.5 units

so, the amplitude of the electric field of the superposed wave will be:

and the phase of this will be:

so, the resultant wave will be written as:

where the phase is now in radians.