The energy of the two waves would not be "cancelled". If this happened, the Law of Conservation of Energy would be violated.
Take waves on an elastic string for exmaple, when the two waves meet, the energy is temporarily stored in the elastic string as potential energy. Such energy will be restoring to the two waves after they separate.
If It Is Constructive Interference,Two Pulse Meets,They Will Produces A New Amplitude,This Amplitude Is Biger Than The Two Pulse.
For Destructive Interference,Two Pulse Meets,They Will Produces A New Amplitude,This Amplitude Is Smaller Than The Two Pulse,
But They Will Cancelled After They Meet,
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