Delay · samples · notches
Comb filter calculator
When one sound reaches two mics at different times, mixing them carves a row of notches into the tone. See exactly where they fall.
Delay and notches
- First notch
- 572 Hzthen every 1,144 Hz
- Delay
- 0.874 ms41.9 samples at 48 kHz
- Path difference
- 30 cm11.8 in · 0.98 ft
- Notches to 20 kHz
- 17each 4.4 dB down, 7.4 dB below the peaks
Sound at 343.3 m/s, 20 °C (68 °F)
What the mix does to the sound
Level of the two copies mixed together, relative to the near one alone. Notches: 572, 1,717, 2,861, 4,005, 5,150, 6,294, 7,438, 8,583, 9,727, 10,872, 12,016, 13,160 Hz, and so on.
3:1 rule of thumb
Under 3:1 The far microphone is 2.50 times as far from the source as the near one (20 cm (7.9 in) and 50 cm (19.7 in)).
By the inverse square law the far copy is about 8.0 dB quieter, so the notches are 7.4 dB below the peaks rather than complete cancellations. Moving the far mic to 60 cm (23.6 in) or more would meet 3:1.
Where the notches come from
Sound covers about 34 cm in a millisecond. If the far mic is 30 cm further from the source, its copy of every sound arrives about 0.87 ms late. Mixed with the near mic, frequencies where the delay is half a cycle cancel, and those where it is a whole cycle add up:
Δt = Δd ÷ c notches at (2k + 1) ÷ (2Δt) peaks at k ÷ Δt
On a log frequency chart the notches crowd together towards the top, like the teeth of a comb. How deep they go depends on how loud the late copy is. In open air its level falls with distance, so the farther mic picks the source up more quietly and the notches are shallower; the calculator estimates that with the inverse square law.
The delay in samples tells you how far to slide one track in your DAW to line the two up for this source. Sounds from other directions arrive with other delays, so alignment helps the main source most.
The 3:1 rule is a rule of thumb, not a law: keep the second mic at least three times as far from the source as the first, which leaves its copy roughly 10 dB down.
Sources
- Comb filtering from a delayed copy, with cancellations at odd multiples of 1/(2Δt) and reinforcement at multiples of 1/Δt: F. A. Everest and K. C. Pohlmann, Master Handbook of Acoustics, 6th edition (McGraw-Hill, 2015), the chapter on comb-filter effects.
- 3:1 rule and the rule of thumb of about 10 dB level difference to keep phasing down: DPA Microphones, 3:1 rule, Mic University glossary.
- Level falls by 20·log10(d2/d1) dB between distances d1 and d2 in a free field (inverse square law): R. Nave, Inverse Square Law, Sound, HyperPhysics, Georgia State University.
- Speed of sound in dry air, c = √(γRT/M): R. Nave, Speed of Sound, HyperPhysics, Georgia State University.
- Inches and feet: NIST Special Publication 811 (1 in = 2.54 cm, 1 ft = 0.3048 m).
Questions
Why does my guitar sound thin with two mics?
Mixed together, the two mics cancel each other at a row of frequencies set by the difference in their distances. Check the mix in mono, try nudging one track by the delay in samples, or move one mic so the notches land somewhere less important.
Does a reflection off the desk do the same thing?
Yes. A reflection is a delayed copy too. Choose “Path difference” and enter how much further the reflected sound travels than the direct sound.
Why are the notches shallower with the 3:1 rule?
At three times the distance the far copy is about 9.5 dB quieter in open air, so it can only take a dip of about 3.5 dB out of the near mic’s sound, against complete cancellation for two equal copies.