calculate combination of sine waves

Question

calculate sine waves

Answer 1

The solution will depend upon

 

1. Total number of sine wave

2. Do they have same or different amplitudes?

3. Do all have same frequency or different frequencies?

4.Do they have phase difference or all have same phase angle at t=0?

5. Are all the waves in the same direction?

After this the principle of superposition of waves can be applied. 

If you answer the above, a solution can be given

Answer 2

If all of the waves are the same frequency, you can use a phasor to represent each sine wave.   Phasor are vectors that represent the amplitude of the sine wave by their direction and the phase of each sine wave by their angle.  You can add up the phasors like vectors -- in a head to tail fashion.  The resulting net phasor (from the origin (where the tail of the first phasor should be drawn) to the head of the last is a phasor that represents the amplitude and phase of the resulting sine wave (which will have the same frequency).

 

If the waves do not have the same frequency, you will get "beats" --  An envelope amplitude that varies at the difference frequency there are trig identities for example sin(A) + sin (B). When A = omega1 * t and B = omega2 * t, these formulas reveal the amplitude envelope and that the combination signal being "beated" has a frequency equal to the average of the two frequencies