# Find the Maximum of Superposition of Waves

1. Nov 13, 2016

### TheDemx27

1. The problem statement, all variables and given/known data
Two waves are produced simultaneously on a string of length L = 1 m. One wave has a wavelength λ of 0.5 m. The other wave has a wavelength λ of 0.2 m. The amplitudes of the waves are the same.

At t=0, at what locations x0 is the displacement y(x0) equal to zero? At what locations xm is the displacement y(xm) an extreme (max or min)? How do these locations change with time?

2. Relevant equations
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3. The attempt at a solution
The superposition can be written as
y(x,t)=A[sin(4*pi(x-vt))+sin(10*pi(x-vt))]

to find the minimums at t=0:
0=sin(4pi*x)+sin(10pi*x)

this i have solved, but to find the critical points at t=0 would mean I'd have to solve

0=4pi*cos(4pi*x)+10pi*cos(10pi*x)

Which I do not know how to solve algebraically due to the coefficients.

Also I do not know how to describe how the locations would change over time.

2. Nov 13, 2016

### kuruman

Not quite. The arguments of the sine functions must be dimensionless quantities.
Also, it would be easier to see what's going on if you used the trig identity for the sum of two signs of equal amplitudes. See here, for example.
http://www.sosmath.com/trig/Trig5/trig5/trig5.html

3. Nov 14, 2016

### haruspex

Did you mean the sum of two sines of unequal magnitudes?