Can adding sound make a plane quieter?

tap the headphone

A plane engine drones outside Nia's ear. Her headphone has a tiny microphone and a tiny speaker. The speaker may add one more sound. Could adding sound make the roar smaller?

one instant of sound

Pressure can rise above or dip below

+ means above the resting air pressure. − means below it. Neither is good or bad.

add at one instant

Two signed pressure values make one total

pressure snapshot+3 + +1 = +4
same signopposite signs

Same-sign values grow. Opposite-sign values leave a smaller leftover.

many instants in a row

Scan the engine's repeating pattern

moment in the dronemoment 1 · pressure +3
first momentlater moment

One full repeat is one cycle. The mic records this amber pattern; the speaker's plan is still blank.

a timing clue

Sent now. Heard later.

follow one pulse1 · send
sendarrive

Sound takes time to travel. A sound sent now reaches your ear later. At the ear, add the sounds arriving together.

the unanswered plan

Try a deliberately delayed speaker

In this toy, the mic reads the engine pressure at the ear. We add a long speaker route: its sound arrives half a drone cycle later. Both plans keep using each new mic reading. What should they send?

A toy test: the speaker route takes half a drone cycle.

Which plan leaves less sound at the ear after that delay?