Bass Amp for Studio

Bigger speakers don't necessarily translate in the studio through a 1" mic diaphragm..   It's fractional wavelengths that you need to be able to reproduce, so a smaller speaker with a larger mic diaphragm is a better solution than a larger speaker alone, at least in a studio situation.

I think you misunderstand the principles behind wavelength theory, and thus also fractional waveform capture and reproduction.  

The wavelength of a 20hz tone is 15,000km..  That's a big speaker if your theory about larger speakers were true.

No speaker actually forms a "complete" cycle at the intended resonant frequency, even in a few feet from the cone.  What you're referring to is amplitude and fractional wavelengths.  Everything from your eardrum to mic capsule only capture a tiny fraction of a waveform's cycle (but in layman's terms) capturing a mathematically significant portion of the signal over time both our brains and our electronics can interpret those rise/fall time constants as part of a larger cycle.  These fractions are usually in some golden mean ratio.  1/2, 1/4, 1/8, etc., are common fractions.  Mathematically they are similar to harmonic content in audio.  I think you're familiar with the "missing fundamental" effect, where the brain "hears" a lower frequency (which does not actually exist) when harmonics of that frequency exist for multiple octaves.  If you've not heard of it, take a look.  It's an interesting effect of psycho-acoustics.

This is well understood in antenna theory, where wavelengths for some RF signals are still measured in dozens of meters, yet the antennas are tiny in comparison.  For instance, a 2.4GHz signal has a whole wavelength of around 5"..  Yet the antennas in your cell phone are usually a little more than an inch..  Because the 1/4 wavelength of 2.4G is 1.25".

Take the dynamic mic vs. the capacitor(condenser) mic for instance.  Lets say that both have a similar 1" diaphragm, but the dynamic's diaphragm moves a lot more in doing it's job than the capacitor mic does, yet both can capture similar frequencies.  If we discount the different mechanics of the systems, each one technically has a moving diaphragm.  The dynamic moves a lot to achieve electromotive force (current) due to it's inherent inefficiency, while the condenser moves a very tiny amount to generate the net charge differential that the FET translates into true current.  In either case, the diaphragm needs not move the same amount as the speaker it's in front of to capture the complete emissions from that speaker, nor does it need to have a diaphragm the same size as the speaker to capture the tones the speaker produces..

This alone disproves the need for wavelengths to develop in space in order to also be able to be captured by a mic, since the inverse is not also true.


However, there is one aspect in driver size that I think you're correct.  Efficiency.  Larger radiators are more efficient at producing lower frequencies, which is why some radiating antennas are still large masts.  It's not necessarily to get the signal to broadcast farther, it's that the mast itself allows a larger wavelength to radiate, and the antenna efficiency is much higher and uses considerably less power. 


A larger speaker will be more efficient at producing lower frequencies, but it's larger size make it less efficient at producing higher frequencies.  The net effect is that you *hear* what can be interpreted as more low frequencies, but the actual physics behind it is simply less high frequencies and higher efficiency at lower frequencies.

Well you're still speaking to the driver and how it relates to how it sounds in the room.  I'm speaking about the capsule of the mic. 


Your theory says that you need a larger speaker to generate lower frequencies, but when turn that theory around it would necessitate needing a mic capsule to be as large as the speaker to translate the same frequencies..


But they don't need to be, as capturing fractional wavelengths using a much smaller diaphragm is exactly what a mic does.

Therefor you don't necessarily need a large cone to generate low frequencies if you're using a mic with a much smaller capsule diameter. 

that's all I'm saying, that you may "hear" lower frequencies in the room, but the mic doesn't necessarily need a large driver in front of it to accurately reproduce the low frequencies.


Personally I'd rather have a smaller driver with faster impulse response, than a larger slower driver, but that's just preference.

True.  If the diaphragm of the mic never changes size, then the fractional wavelength it can "see" never changes, so the absolute waveform doesn't matter, as long as the component of the waveform you're trying to capture is within the output waveform..  That's what I kept trying to get across to John.    A good example is EQ..  Even through small speakers, you can bump the EQ on the low end and hear an apparent increase in low frequencies to the point that they could equal the bass output of a larger speaker, but rather inefficiently.

What happens when you place a mic closer or further is simply phase cancellation, not a "developing" waveform.

4x10 bass cab will sound A-OK close mic'd. That is all I am commenting on, sir and I am well qualified to hold that opinion. I am not impugning your knowledge or wanting to have a physics fight with you— that's Svart's job. (And hats off to you, live sound is such a sad, thankless job most of the time.)

Ok, lets step back a second before talking about ears and mics..

What you've described with colliding wavefronts(waveforms) is creating an additive and mixing effect.  Highs are being attenuated due to distance and the power taken from their reflections while the lows are "thickening" through frequency and amplitude mixing. 

Time delay due to reflections is essentially frequency delay (think of the doppler pitch change with a train horn going by) due to path length differences from reflected surfaces and straight line travel at different frequencies.    This is also how room modes happen, and how certain areas in rooms will have boomy bass..  Because the summation of frequencies at that location are additive in amplitude, but nothing about the original waveform "developed" at all.  The true waveform frequency and amplitude exited the speaker cone at the original magnitudes, and why so many people spend huge amounts of money to dampen room modes with absorption and proper room geometry to mitigate reflection-related frequency mixing.

 So in summary, you're not hearing a "developing" waveform, you're hearing the summation of multiple waveforms that result in an addition amplitude in frequencies that either did not exist prior, or did not exist at those magnitudes in the original source waveform.  You can account for this by lowering the frequencies of interest at the source, but it's still not the same thing.

So that comes back to the mics and ears..  While there is a moving diaphragm in both, the ear has a very nonlinear mechanical compression aspect that de-accentuates the effect of low frequencies and allows us to hear them without considerable distortion , aka the "loudness" curve that mics do not have. 

Ears are very non-linear, while mics are almost entirely linear, which unfortunately makes them very bad at dealing with low frequencies before distortion.  Ears also have a built-in waveguide (ear canal) that has evolved to boost frequencies around 2K-3K and attenuate highs and lows, which increases intelligibility of the human voice.  It also acts as a rudimentary polarization filter, so that only waveforms from one direction may enter, increasing directionality and reducing frequency mixing products and distortion.

But back to the discussion at hand..

You say that lows need room to develop, but I've been asking if that were true, then how can a mic with a tiny diaphragm (compared to the size of the waveform) capture such a large waveform that needed the large space to develop?  If you need 15" of speaker cone and an auditorium to create a signal at low frequencies, then by the inverse of that belief, the 1" mic diaphragm could never capture that waveform at all..

And that's the question I've been wanting you to answer..  But I know the answer already, and I've stated it multiple times here in this thread.  It's called fractional wavelengths, and it's well explained in antenna theory, but the theory is almost never explained in the audio design world.

A waveform at a specific frequency always has a specific rise and fall time during it's 360deg cycle.   As long as you can capture a fractional component of that waveform's rise/fall times, then you can extrapolate the frequency of that waveform, even without "seeing" the whole waveform through the 360 degree cycle, or even seeing it's total amplitude..  This is why a mic diaphragm (or the human ear) can hear frequencies with waveforms that are much, much larger in both amplitude and wavelength than would be possible if we only considered the size of the radiating device(speaker) to the small diaphragm used to capture those frequencies(wavelengths).

It's the same as sampling theory in analog/digital converters..  You take tiny snapshots in time, and you capture values of the waveform at specific times with which you can then recreate the waveform based on the timing and the values.

A mic's diaphragm has a specific mass and size, which work together to make a specific frequency response.  Knowing the reaction of the mass/size over time and frequency, you can electrically reproduce waveforms that are much larger than the small size would normally resonate at, all based on the reaction timing of the diaphragm..  AKA "tuning" the capsule.

So no, a mic does not need for a waveform to "develop" in the room to capture the true signal from a speaker at the original amplitudes of the signal.  

If you're counting on the room creating an EQ effect to boost low end, that's not "developing" a waveform, that's using additive mechanical EQ.   If you're a live engineer and you account for the room boost and reduce low frequencies so that the buildup in the room becomes normal, that's not allowing a waveform to "develop" either, that's de-emphasis to account for a poor acoustics that cause additive frequency summation.  

Look, I'm not saying what you hear isn't real, I'm just saying that your explanation is applying the theory incorrectly and coming to the wrong conclusions. 

I think it's the same thing, but coming from different angles of explanation of the resulting effect.

John is saying that there needs to be space between a speaker and a mic to allow a waveform to develop, but I'm saying that the mic only sees a tiny portion of any waveform at any one time due to the inability of a small diaphragm to move the same distance of the full wavelength, and therefor doesn't need "space" at all and that the effect of hearing more bass in a given space is purely an effect of additive frequency mixing accentuating the low end frequencies, AKA: low end build-up.

A speaker has a finite excursion, and the two ends of the excursion define the minimum frequency that the driver can create at a given amplitude.  Larger drivers are more efficient at creating lower frequencies at higher amplitudes, but smaller drivers can recreate the same lower frequencies with longer excursions at the expense of much higher power consumption.

In any case, the driver excursion is not sufficient to satisfy creating a full low frequency waveform that could be multiple meters long, so what it creates is fractional wavelengths that our ears (and mics) interpret as being part of a full wavelength due to the rate of rise/fall of the waveform over a given time.   

So lets say that 20hz sinewave has a wavelength of 56FT.. Because it does.. 

To properly recreate the sinewave fundamental, the speaker would have to have an excursion that totalled 56FT, so 28FT inwards, and 28FT outwards..  No speaker that I know of has that kind of excursion, so no speaker can truly recreate a lossless fundamental waveform of 20Hz, regardless of how much space is in a room.   Lets say that a speaker of a given size can move about 2.6" in total excursion, which relates to around 1/256th of a wavelength..  Which means that the power at that fraction is very low, but if the speaker is sufficiently tuned for resonation at or near that frequency and the driving power at that frequency is sufficiently large, one could still recreate enough of the 20hz wavelength to be perceptable by the human ear and interpreted by the brain as 20hz.