# Check 2 waave displacement equations please!

1. Mar 22, 2012

### Lengalicious

Got to calculate the superposition of a couple o' waves, wanted to double check if they are both the same frequency and wavenumber?x1(t) = 3 sin(2t + /4 ) and x2(t) = 3 cos(2t).

I take it 2 is the frequency? And since Kx is not inside the function how can I know whether the wave numbers the same? :S

2. Mar 22, 2012

### nasu

These are not waves. The equations have to spatial variable. They may represent two harmonic oscillations with a phase difference of pi/4.
2∏ is the angular frequency, ω=2∏f. The frequency is 1 Hz.

3. Mar 22, 2012

### Lengalicious

Ok thanks, when 2 harmonic oscillators superpose do you just take the sum of the two even though they have different phases?
EDIT: Since one is in terms of sin and the other in cos, do i make sin(2pit+pi/4) into cos(2pit+pi/4+pi/2) or is that not valid, cuz i need to use the trig sum-product identity

Last edited: Mar 22, 2012
4. Mar 22, 2012

### Khashishi

Yes, you add the functions. You don't need a trig sum-product identity. Use the phase identity sin(x) = cos(x-pi/2)

5. Mar 22, 2012

### nasu

Depends what you mean by the "take the sum".
At any time, the total displacement is the sum of the two displacements (superposition principle):
x(t)=x1(t)+x2(t)
If you wish you can try to simplify or otherwise put the expression into a different form that shows something interesting.
You cannot use the trig identity as the two have difefrent amplitudes.
For the given case, you can write the result as a single cosine or sine,
x(t)=Asin(2∏t+ψ).
To find the values of A and ψ you can expand the sin and and identify the terms with the original components. You'll find two equations in the variables A and ψ.
Phasor algebra is a more straightforward method, if you are familiar with it.