1. The problem statement, all variables and given/known data Two waves on a string are given by the following functions: Y1 (x,t) = 4cos(20t-x) Y2 (x,t) = -4cos(20t+x) where x is in centimeters. The waves are said to interfere constructively when their superposition |Ys| = |Y1 + Y2| is a maximum and they interfere destructively when |Ys| is a minimum. if t = ∏/50 seconds, at what location x is the interference constructive? 2. Relevant equations No particular equation relevant as far as I know. 3. The attempt at a solution So to get a constructive interference, the summation of the two waves(|Y1 + Y2|) must be the largest possible. I plugged in the value for time, and got this simplified equation for Ys: Ys = |4[cos(2∏/5 - x) - cos(2∏/5 + x)]| Now i know |Ys| must be the largest it can be, and the only way i can think of of approaching this is constructing a X-Y table and seeing if there is a trend in the values, though I feel there must be an easier way to do this.