# Wave Superposition Problem

1. Feb 6, 2005

### pulau_tiga

Hi,
I'm having some difficulty getting the correct answer for a problem relating to wave superpositiong.

Question: Two waves in one string are described by the wave functions
y1 = 3.15 cos (3.65x - 1.40t)
and
y2 = 4.10 sin (5.05x - 2.20t)
where y and x are in centimeters and t is in seconds. Calculate the superposition of the waves y1 + y2 at the points x = 1.50, t = 1.30. (Remember that the arguments of the trigonometric functions are in radians.)

I simply added y1+y2, after evaluating each at the given points.
ytotal=3.15cos(3.655) + 4.10sin(4.715)
=-6.84 cm.
-6.84, and 6.84 is not the correct answer.

I then, reasoned that since sine and cosine waves are out of phase by 90 degrees, to add pi/2 to one of the functions.
Which resulted in.
y1=3.15cos(3.655) and y2=4.10sin(4.715 + (pi/2) )
ytotal = -2.73.
This is not correct either.

If anyone could help me, or point me in the right direction to how you solve the problem, it would be greatly appreciated.

Thanks.

2. Feb 6, 2005

### Integral

Staff Emeritus
Double check your arithematic, I did not get the same result as you. You may wish to show us the detalis of your calculation.