Wave-Wave Interactions: Adding waves as vectors using phasor technique

Every sinusoidal wave of a given frequency can be thought of a two-component vector, characterized by and amplitude and a phase. When adding two or more sinusoidal waves, one adds them as vectors. The amplitudes DO NOT simply add! One can get two waves to partially or fully cancel each other when they are added together.

In the applet below you can change the amplitude and phase of a traveling sinusodal wave. The wave can be constructed by plotting the vertical component of a vector as it rotates counterclockwise. Notice how phase shifts change the orientation of this vector whereas amplitude changes modify its length. Stop the traveling wave to look at how phase and amplitude changes affect the wave. Run the wave to see how it travels.

Now what happens when two traveling waves of the same frequency are added. The amplitude and phase of the final wave is simply the sum of the vectors making up the individual waves. Here phase plays an important role, as the individual vectors can cancel. In the applet below you can change the amplitudes and phases of the individual waves (W1 and W2) to get the final wave (Tot). Note that the the vector representing the final wave rotates at the same frequency as the individual waves and that the final waveform is determined by plotting the vertical component of the total vector versus time. In the applet below you can see how the individual waves add as vectors to form a new wave, which is also represented by a vector.

Use the above simulation to answer the questions in the pop-up window quiz.