Destructive Interference

When Wave B's trough lands on Wave A's peak, equal-and-opposite pressures sum to a flat line: silence.

What it is

Two sound waves with opposite timing collide and cancel each other, dropping the volume or killing it dead.

Key facts

• Full cancellation needs waves 180 degrees out of phase (half a cycle late) AND equal level: a perfect null = silence
• Speed of sound in air = 343 m/s at 20 degrees C (rises ~0.6 m/s per +1 degree C)
• Wavelength: lambda = c / f, where lambda = wavelength (m), c = speed of sound (343 m/s), f = frequency (Hz)
• 100 Hz wave = 3.43 m long, so 1.715 m of path difference (half) nulls 100 Hz
• 1 kHz wave = 0.343 m, so just 17 cm of path difference nulls it
• 180 deg of phase = a delay of half the period; period T = 1/f seconds
• Two equal waves IN phase add +6 dB (double pressure); fully OUT of phase = zero (minus infinity dB)
• Comb filtering = repeating peaks and nulls from one delayed copy; notch spacing (Hz) = 1 / delay (s)
• A 1 ms reflection notches at 500 Hz, 1500 Hz, 2500 Hz... and -3 dB = half power (0.707 of pressure)
• Reversed speaker polarity (+/- swapped) inverts the whole signal, 180 deg out: broadband bass cancels

How it works

1. Sound A and sound B arrive at the same point in the room or mic
2. If B's high-pressure peak lines up with A's low-pressure trough, they push opposite ways
3. Equal-and-opposite pressures sum to zero, so the eardrum or mic feels nothing
4. Caused by a time delay, a longer path, a reflection, or reversed speaker polarity
5. The closer to 180 deg out and the better the level match, the deeper the cancel
6. Change frequency, position, or delay and the cancel point moves

Real examples

• A miswired speaker (+/- swapped) on one side makes bass thin out in the middle of the room
• Two subs spaced apart leave a dead zone where their paths differ by half a wavelength
• A vocal mic plus its reflection off a music stand causes hollow comb-filter colouring
• Noise-cancelling headphones play an anti-noise wave 180 deg out to erase engine drone
• Stand at a room mode null and the kick drum almost vanishes, two steps away it booms

How it helps in live sound

• Check speaker polarity FIRST: a flipped +/- cable cancels bass between boxes, fix with a known-good cable or polarity flip
• Set subs in a centre cluster or cardioid array to avoid half-wavelength dead zones across the crowd
• Mind the 3:1 rule: keep mics 3x further apart than each is from its source to limit cancellation
• When stacking sub + tops, time-align with delay so the crossover adds (+6 dB) instead of nulling
• Use a measurement mic + Smaart/REW to spot comb-filter notches, then move the mic or speaker
• Walk the room with pink noise before doors: find room-mode nulls and reposition subs or seating away from dead spots