# Homework Help: Constructive Interference Problem in the Time Domain

1. Apr 4, 2012

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.

2. Apr 5, 2012

### Staff: Mentor

Yes, there is an easier way. If you add two sinusoidal functions that are in phase, what is the maximum amplitude that you can get?

y = Asin(∅) + Bsin(∅)

What is the amplitude of y?

So it's the same situation when you have constructive interference...