Question

Two sounds waves could never intefere in such a manner as to cancel eachother out and proudce silence.

Answer 1

Your sentence is incorrect. Two sound waves can cancel each other by destructive interference, but there are important limitations.

Short explanation
- Superposition: sound pressures add. If p1 + p2 = 0 at a point, you get zero pressure fluctuation (silence) there.
- Condition for exact cancellation at a point: the waves must have the same frequency and amplitude and be exactly out of phase (phase difference of π), and they must arrive at that point coherently.
- Cancellation can be local, not necessarily global: you can get silence at some points in space (nodes of a standing wave) or in a limited region (as in active noise‑cancelling headphones), but you cannot generally cancel a sound everywhere in space for arbitrary sources and frequencies.

Examples and caveats
- Standing waves: two equal-amplitude waves traveling in opposite directions produce nodes where pressure is zero.
- Active noise cancellation: headphones measure external noise and generate an inverted waveform; this produces cancellation near the ear but not throughout the room.
- Global cancellation is practically impossible for arbitrary sounds because you would need to match amplitude and phase at every point in space and for all frequencies. Also, energy isn’t destroyed — it is redistributed or absorbed (the sources producing the inverted wave may absorb power).

If you want, I can:
- Correct the sentence for you, or
- Show the simple math (wave equations) that demonstrates cancellation, or
- Describe how active noise cancelling works in more detail. Which would you prefer?