Energy in destructive interference.

[AlchemistK]

Homework Statement

What happens to the kinetic energy of the system when two pulses interfere destructively?

Exact Question:

Two pulses in a stretched string whose center are initially 8 cm apart are moving towards each other as shown in the figure(Attached). The speed of each pulse is 2 cm/s. After 2 sec the total energy of the pulse is
a)zero
b)purely kinetic
c)purely potential
d)partly KE and partly PE

Homework Equations

-

The Attempt at a Solution

When two pulses collide, they interfere, either destructively or constructively, depending on their phase difference. In this case they will interfere destructively and if the amplitudes are equal, they will completely cancel each other out.
But where did the energy go?

What exactly goes on at the time of the interference? Does the energy temporarily get converted into potential energy?

 

[Redbelly98]

Keep in mind that two things can be happening to the string at any time:

(1) it can be stretched, i.e. displaced from the equilibrium position
(2) it can be in motion, i.e. moving up and down.

Thinking about these questions should help you get the answer:

Which one of the above is associated with potential energy?
Which of the above goes with kinetic energy?
And finally,
Is one of the above definitely not present at the moment there is complete destructive interference?

Answering that last question should lead you to the answer.