(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Two displacement waves with the same period T = 3.0 s are described mathematically by:

y_{1}= (10.0 m) cos[2πt/T + π]

y_{2}= (9.0 m) cos[2πt/T + 2π]

What is the resultant displacement at time t = 6.0 s?

3. The attempt at a solution

I tried adding up

y_{1}+ y_{2}= 19 cos [2πt/T + 3π]

But the answer I get is wrong. I also tried the following formula from my texybook which is supposed to give the resultant of two traveling sinusoidal waves:

[tex]y=2Acos \left( \frac{\phi}{2} \right) sin \left( kx-\omega t + \frac{\phi}{2} \right)[/tex]

I don't know what the phase constant (φ) is, so I assume it is zero since the waves are in phase, then cos(φ/2)=cos(0)=1.

When I plug in the numbers the formula then becomes

y=6sin(3π+2π6/3)

Again, this produces the wrong answer, the correct answer should be -1.0 m. What's wrong with my calculations?

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# Homework Help: Superposition problem help

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