frequency range for instrument vs speaker

>After seeing this link in another thread, I wonder about this. Let say that you don't listen to any classical instrument/music, normal rock and pop with no heavy synthetizer, just drum, guitar, etc, it seems that there isn't really any need for speakers that go much below 40Hz, considering that the lowest instrument, the kick drum (I assume it is the same thing as bass drum?) only go down to 50Hz.

You may still want speakers that play much lower because you need larger drivers for dynamics at higher bass frequencies and the consumer market expects such speakers to have low frequency extension which makes getting one without the other difficult.

Maximum excursion limited SPL from a monopole operating into free space at 1 meter is

102.4dB + 20log(displacement) + 40 log(f) with displacement in m^3

or

102.4dB + 20log(travel) + 20 log(area) with travel in meters an area in meters^2 if you prefer.

Output at the maximum linear excursion into full space for various representative drivers one meter away is as follows at 120, 80, 40, and 20Hz. Many drivers have less excursion and lower output. Subtract 3-5dB getting to your listening position in a typical living and more for a larger space.

You can add 6dB for a floor mounted woofer (as in many 3-ways), 6dB if there are a pair of bass drivers, and 6dB at the cross-over point to a sub-woofer.

Size Driver Sd (cm^2) x xmax (mm) 120Hz 80Hz 40Hz 20Hz
4 1/2" Seas W12CY001 50 x 3 89dB 82dB 70dB 58dB
5 1/4" Peerless 830873 88 x 3.5 95dB 88dB 76dB 64dB
6 1/4" Seas L16RN-SL 104 x 6 101dB 94dB 82dB 70dB
7" Seas W18EX001 126 x 5 102dB 95dB 83dB 71dB
8.5" Seas W22EX001 220 x 5 106dB 99dB 87dB 75dB
10" Peerless 830452 352 x 12.5 118dB 111dB 99dB 87dB
12" Peerless 830500 483 x 12.5 121dB 114dB 102dB 90dB

Where jazz sounds great at 85dBC average and good recordings have 20dB of dynamic range peaks are hitting 105-107dB a meter from each speaker. Feeding _Take Five_ through 60Hz second order Butterworth IIR low-pass filters I noted right channel low frequency peaks 10dB down from that; although that's still 30 times the acoustic power you can squeeze out of a 6" driver at 40Hz.

You may even want sub-woofers in spite of not being a bass-head. They're one way to get displacement past 100Hz without compromising with a larger mid-range that won't mate as well to most conventional dome tweeters. They let you have the SBIR bass null caused by the front wall reflection (at 1130 / 4 / distance in feet which is 70Hz at 4 feet and 57Hz at a more audiophile friendly 5 feet) out of the speakers' pass-bands. Multiple sub-woofers are also an effective way to minimize the big peaks and nulls you get below the room's Schroeder frequency somewhere in the 100-200Hz range for most domestic spaces.

Other points about low frequency extension are that

1) It's not a brick-wall. Extension to 50Hz generally means that output is at least 3dB down at that point with a noticeable 1dB of drop up much higher like at 80Hz.

2) The effects are worse than the numbers would suggest due to the equal loudness curve spacing at low frequencies. Once you get to 50Hz at moderate listening levels 3dB is like 6dB down at 1KHz which is 1/4 the acoustic power and quite significant (a full 10dB gets you a perceptual halving of volume).

3) The -3dB extension does not imply that the speaker is actually flat to that point. Many small speakers have a bump in frequency response (a few dB) which boosts the harmonics of low frequency instruments and can either give the impression the missing frequencies are still there or make the speaker sound boomy depending on what they're trying to reproduce. This design choice is more likely in speakers with less low frequency extension.

06-22-12: Onhwy61
>I think Frogman is correct, but it should be put into perspective. Suppose you were an audiophile with limited funds. Would you be better off pursuing bass response down to 20Hz, or compromise at 50Hz (with room reinforcement) and put more money into going for a better quality midrange and treble? Unless you're an absolute bass fanatic the answer is self-evident.

The answer is counter-intuitive and not at all self-evident without a far better understanding of acoustics and psychoacoustics than the average audiophile's. The combination of physics and consumer market expectations make getting quality midrange without last octave extension unlikely so seeking good high frequency performance means looking for the same things that give you lower bass.

Beyond a room's Schroeder frequency (100 - 200 Hz in typical domestic rooms) and assuming the speaker is correctly voiced for your chosen placement with respect to room boundaries how natural a speaker sounds comes almost entirely from

1. Its polar response with the ideal being flat on-axis with directivity increasing monotonically with frequency. Our brain determines timbre from the spectra of what it believes to be a direct sound and its delayed reflections. An increase in reflected high frequency energy isn't consistent with natural sources (directivity increases with frequency) and environments (natural materials like foliage absorb and diffuse more at high frequencies where they're becoming acoustically large) and doesn't sound right.

This comes predominantly from the driver/baffle sizes/shapes you use including options to increase directivity from an acoustically small driver with a wave guide or cancellation from acoustic dipoles and cardioids.

Untamed driver and cabinet resonances can also play a negative role, showing up as amplitude peaks at all angles.

2. The distortions which go with approaching and exceeding a driver's linear limits. Harmonic distortions change the timbre and IM distortion adds non-musical sounds that weren't in the recording and damage the midrange.

Unfortunately you can't build a flat baffle 2-way with conventional cone and dome drivers which does well in both areas. When you compromise with a smaller mid-range to get better polar response you lack the displacement needed for clean reproduction of lower frequencies (250Hz is probably a nice lower limit for a 4" driver, 150 Hz 5", 120Hz 6-7", 80Hz 8.5", 40Hz 10"). When you compromise with a larger midrange to get clean output at acceptable listening levels you end up with a noticeable harshness resulting from the significantly broader dispersion crossing to the tweeter at 2-4KHz or beyond. People work around that with some success using a drop in output in the range (the BBC dip) although the resulting speaker is more sensitive to the room (you'll notice the lack of energy in a large/absorbing room because there's less compensation for the on-axis dip) than a speaker built with more uniform directivity.

Sticking to flat-baffled vaguely box-shaped speakers that most consumers shop for the solution is at least a 3-way, whether in one cabinet or separate boxes. 120Hz and beyond can work well crossing to stereo "sub-woofers" which are better described as woofers, although if terms like "pole", "zero", and "biquad" aren't in your vocabulary that probably won't end well as a DIY exercise.

Once you do that the extra extension has negligible additional parts cost, although it costs you 9dB of efficiency for the same cabinet size or a box 8X as big at the same efficiency. Most consumer speaker company marketing departments compromise with lower bass to satisfy more listeners, smaller cabinets for spouses, and less efficiency.

The intuitive but incorrect counter-argument is that you're better off with fewer more expensive drivers. It fails because a pair of drivers in a conventional configuration have audible and measurable problems from their inherent physics that more appropriate sized less expensive drivers with lower total cost (and better sound) do not.

Whether you're spending $200, $2000, or $40,000 on drivers flatter on-axis and more monotonic polar response sound more similar than different. Deviating from that design goal is not good although the specific failings vary. It's like Tolstoy's comment "Happy families are all alike; every unhappy family is unhappy in its own way."

06-22-12: Onhwy61
>I think Frogman is correct, but it should be put into perspective. Suppose you were an audiophile with limited funds. Would you be better off pursuing bass response down to 20Hz, or compromise at 50Hz (with room reinforcement) and put more money into going for a better quality midrange and treble? Unless you're an absolute bass fanatic the answer is self-evident.

The answer is counter-intuitive and not at all self-evident without a far better understanding of acoustics and psychoacoustics than the average audiophile's. The combination of physics and consumer market expectations make getting quality midrange without last octave extension unlikely so seeking good high frequency performance means looking for the same things that give you lower bass.

Beyond a room's Schroeder frequency (100 - 200 Hz in typical domestic rooms) and assuming the speaker is correctly voiced for your chosen placement with respect to room boundaries how natural a speaker sounds comes almost entirely from

1. Its polar response with the ideal being flat on-axis with directivity increasing monotonically with frequency. Our brain determines timbre from the spectra of what it believes to be a direct sound and its delayed reflections. An increase in reflected high frequency energy isn't consistent with natural sources (directivity increases with frequency) and environments (natural materials like foliage absorb and diffuse more at high frequencies where they're becoming acoustically large) it doesn't sound right.

This comes predominantly from the driver/baffle sizes/shapes you use including options to increase directivity from an acoustically small driver with a wave guide or cancellation from acoustic dipoles and cardioids.

Untamed driver and cabinet resonances can also play a negative role, showing up as amplitude peaks at all angles.

2. The distortions which go with approaching and exceeding a driver's linear limits. Harmonic distortions change the timbre and IM distortion adds non-musical sounds that weren't in the recording and damage the midrange.

Unfortunately you can't build a flat baffle 2-way with conventional cone and dome drivers which does well in both areas. When you compromise with a smaller mid-range to get better polar response you lack the displacement needed for clean reproduction of lower frequencies (250Hz is probably a nice lower limit for a 4" driver, 150 Hz 5", 120Hz 6-7", 80Hz 8.5", 40Hz 10"). When you compromise with a larger midrange to get clean output at acceptable listening levels you end up with a noticeable harshness resulting from the significantly broader dispersion crossing to the tweeter at 2-4KHz or beyond. People work around that with some success using a drop in output in the range (the BBC dip) although the resulting speaker is more sensitive to the room (you'll notice the lack of energy in a large/absorbing room because there's less compensation for the on-axis dip) than a speaker built with more uniform directivity.

Sticking to flat-baffled vaguely box-shaped speakers that most consumers shop for the solution is at least a 3-way, whether in one cabinet or separate boxes. 100-120Hz works well crossing to stereo "sub-woofers" which are better described as woofers, although if terms like "pole", "zero", and "biquad" aren't in your vocabulary that probably won't end well as a DIY exercise.

Once you do that the extra extension has negligible additional parts cost, although it costs you 9dB of efficiency for the same cabinet size or a box 8X as big at the same efficiency. Most consumer speaker company marketing departments compromise with lower bass to satisfy more listeners, smaller cabinets for spouses, and less efficiency.

The intuitive but incorrect counter-argument is that you're better off with fewer more expensive drivers. It fails because a pair of drivers in a conventional configuration have audible and measurable problems from their inherent physics that more appropriate sized less expensive drivers with lower total cost (and better sound) do not.

Whether you're spending $200, $2000, or $40,000 on drivers flatter on-axis and more monotonic polar response sound more similar than different. Deviating from that design goal is not good although the specific failings vary. It's like Tolstoy's comment "Happy families are all alike; every unhappy family is unhappy in its own way."

06-23-12: Stringreen
>Richard himself helped me with my setup and told me that the goal was NOT to get a flat frequency response...just s pleasing one.

That's an over-simplification.

As an engineer I have built speakers with acoustically small drivers and baffle sizes decreasing with frequency for a flatter first derivative of amplitude with respect to frequency off-axis.

Richard does the same, spending more on labor than he would with rectangular cabinets and then wraps the result with a cosmetic grill-frame producing more conventional aesthetics he can sell.

I can't come up with technical reasons for him to do that apart from the same pursuit of measurable "flatness" whether he quantifies it like that or the result just sounds better.

>Flat frequency response is a-musical.

That's wrong.

Your brain is looking for flat response in the direct sound with less high frequency content in the reflections. That's what you get from live un-amplified performances in good venues which should be the reference for sound reproduction. Any more real would be surreal.

When you feed such ideal signals to a SPL meter it doesn't look at the time domain and just averages everything together. It will and should show a roll-off towards high frequencies. It also picks up wiggles from combing which are often not perceptually important.

Trying to correct what the meter sees can ruin the things the speaker is doing right.

Amplitude adjustments around directivity minima can make things subjectively more natural and flatter (the BBC dip), although simple measurements may not show that's what's happening.