By Richard Campbell
“Bass in the Brain”
I own a Bose wave radio because I need to hear my mastering efforts on it (in addition to the studio monitors)–and it is convenient. But as the woman in their ad asks, “How do they do that?”
The sensation of sound pressure at a distance from a circular piston in an enclosure is proportional to the volume velocity of the source (cubic meters per second) times the frequency for a fixed distance.
Let’s take a peek at an equation defining the pressure at a distance from a loudspeaker in an infinite baffle (rho is the density of air):
p(r) = |U|*f*rho/r in words, the volume velocity times frequency times density all divided by distance equals the pressure.
The density of air is ~1.3 kg/m3. Let’s say we are trying to achieve 0.3 Pa pressure (~84dB SPL) at a distance of 3m. At 100Hz, and solving for |U|: 0.3/((100*1.3)/3) = 0.0069 m3/s which is 69 cm3/s.
Assuming we have a small driver, say 5cm (effective) diameter, the area will be 19.6cm2. To develop the above volume of 69 cm3 requires a piston movement of 3.5cm!
Oh oh, we have a problem. One popular driver in this size range can move +/- 0.5 cm. That limits the volume displacement to +/- 34.5 cm3. That suggests that something around 200Hz will be the LF limit for the driver (given that other variables do not change).
Of course, a certain amount of back loading using an acoustic labyrinth can control some of the driver displacement, but the volume velocity somehow has to be achieved – either from the driver or the labyrinth port — or does it?
The “missing fundamental” is a well known psychoacoustic phenomenon. When we hear an array of harmonics that suggest there must be a fundamental somewhere – we hear the fundamental in our brain. Can’t live without it!
So here comes a low note from the CD on the way through the audio system to the loudspeaker. There is a low-pass filter on the audio side, say 100Hz cutoff, and when a signal comes through this filter there must be a note present below 100Hz. Its frequency is determined and an array of harmonics is created to make the listener think that the note is actually there on the acoustic side. These harmonics are then discreetly fed into the main audio stream for the length of the note.
To my knowledge, the first company to offer this was WAVES with their MAXXBASS products. I had their first demo CD that allowed the user to select the high-pass filter on the main audio stream. Then select how much bass you wanted to hear. Wild!
However, I got used to listening to this ‘fake’ bass and aurally separate it from ‘real’ bass, such as a string bass in an A-B test. But under normal condition of simply listening to music it does not do a bad job. As WAVES says:
“…if you are mixing for a specific system, such as a kiosk, theme park, commercial sound installation, special radio mixes, etc., you can extend the range of that system by replacing almost all of the original bass signal with the MaxxBass signal.”
And that’s how they do that!
Footnote — forget the values, just go for the units to see if they come out right!
p(r) = |U|*f*rho/r
[a] (m3/sec * 1/sec * Kg/m3 ) / m is definitely a mouthful of units, but it immediately reduces to
[b] Kg/sec2/m. Remember F = M*a from physics 101? So,
[c] M = F/a which is Newtons/m/sec2
Substituting [c] into [b] gives us N-sec2/m * m/sec2 * 1/m = N/m2 = pressure – right!