Superposition of Radio Waves
Question:
We are taught to count the number of squares under two waves and
add them up as the superposition wave. But are there any better
ways of drawing the final superposition wave?
I just wonder if a sine wave is added with another sine wave
(of different amplitude and frequency), will the resultant be
another sine wave? Is there any calculations to show it? I
don't take Math's so I don't know how to check
it.
Answer:
The superposition of two sine waves has as its amplitude at any
time the sum of the amplitudes of the two component waves at that
time. Simply counting the height of each component wave from a
graph and adding them is an acceptable way of getting the
superposition. It is quick and reasonable accurate. A more
precise way involves writing the superposition wave function as
the sum of the wave functions of each component. Each of the
component wave functions will depend on time so you may get the
value of the superposition at any time by substituting that value
of time in the superposition function and calculating the
superposition amplitude.
As an example of the mathematical calculation of the
superposition, suppose we had two wave functions:
f(t)=2*sin(2*t) and g(t)=3*sin(3*t) The
superposition of these two waves of different amplitude and
frequency would be: s(t)=2*sin(2*t) + 3*sin(3*t)
Now for any time t you can calculate the value of the
superposition. The wave form of the superposition of waves of
different amplitude and frequency is quite complicated and not
easily visualized based on a graph of the component waves. It
will not be a simple sine wave.