Can adding sound make things quieter?

Find the quiet point

Change the phase of the second wave.

Together

Matching peaks reinforce each other.

Partly shifted

The combined amplitude changes.

Opposite

Equal opposite disturbances cancel in this ideal model.

Equal frequency and amplitude; linear superposition. The optional sound is a synthetic tone, not a recording or a headphone test.

What you just noticed

Superposition adds disturbances point by point. Cancellation requires the right amplitude and timing at the observation point. Real rooms and broadband noise are more complicated.

Keep the distinction