Constructive and Destructive Interference of Waves at pi/50 Time - Find Points

[Tom McCurdy]

Homework Statement

y1(x,t)=4*cos(20*t-30*x)
y2(x,t)=4*cos(20*t+30*x)
set t=pi/50 and find the points where the wave interferes constructively and destructively

The Attempt at a Solution

So I tried to take the derivative of y1 and y2 added together and set it equal to zero.

$$120*sin(\frac{2 \pi}{5}-30x) = 120*sin(\frac{2 \pi}{5}+30x)$$

then I took out the 120 on both sides, but I am not sure what to do from their exactly. I tried to take the arcsin a few different ways but I couldn't get anything concrete.

I know the answer is $$x= \frac{\pi}{60}+\frac{2 \pi n}{30}$$ for constructive
and $$x= \frac{n \pi}{30}$$ for destructive

this makes sense to me since the period would be 2pi/30 but I don't get how they actually got there. Could someone point me in the right direction

 

[Mindscrape]

Since both of these waves have the same amplitude and the same angular frequency when they interfere they will give 0 for destructive interference and wave*2 for constructive.

wave1 + wave2 = 0 happens when?

how does the constructive go?

think about what a phase really means