10.1.2 Phase Difference

In the previous section, we saw how two pulses can superpose. Actually, the H2 syllabus is mostly concerned with the superposition of continuous sinusoidal waves (drawn in red and blue below).

It turns out that when two sinusoidal waves (of the same period) superpose, the resultant wave is yet another sinusoidal wave (with the same period). If the amplitude of each superposing wave is A, then the amplitude of the resultant wave can range from 0 to 2A, depending on the phase difference (between the two sinusoidal waves).

If the phase difference between the two sinusoidal waves is 0, 2π, 4π, 6π and so on, the two wave profiles will be exactly aligned to each other. The two waves are said to superpose in-phase. We are looking at a constructive interference and a resultant wave of amplitude 2A (shown in magenta).

If the phase difference between the two sinusoidal waves is π, 3π, 5π, 7π and so on, the two wave profiles will line up exactly opposite to each other. They are said to superpose in antiphase. We are looking at a destructive interference and a resultant wave of amplitude 0.

What if the phase difference is some in-between value? Well, the outcome will still be a sinusoidal wave, but the amplitude will be between 0 and 2A. For example, when the phase difference is 0.5π, the resultant amplitude is $\sqrt{2}A$ . (You may have learnt the $R\sin (\theta +\alpha )$ formula from H2 Math? So $\sin x+\sin (x+0.5\pi )=\sqrt{2}\sin (x+0.25\pi )$ )