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Homework Statement
Two pulses of the form
e^-(x + 4)^2
e^-(x - 2)^2
travel in opposite directions along a tensed non dispersive rope. If the speed of propagation of both pulses is 2 cm/s, find the instant of time in which the wave's amplitude goes to zero, if it exists.
Homework Equations
I am supposed to replace x with x - vt & x + vt for each of the pulses, respectively (I would have never guessed), then set their sum equal to zero.
The Attempt at a Solution
I've got e^-(x -2t + 4)^2 + e^-(x +2t -2)^2 = 0
and need to find the value of t that satisfies the equality (if it exists, which it does btw)
I feel like I don't know enough about exponentials and logarithms to solve this. They're gaussian curves not complex exponentials so I can't expand them into cos and sin arguments and play around with those to see what gives me a 0.
I tried expanding the polynomial in the exponents but it didn't seem to get me anywhere. How do I solve this type of problem?