Subwoofer Room Pressure - spl or freq? - AVS Forum | Home Theater Discussions And Reviews
Forum Jump: 
 
Thread Tools
post #1 of 5 Old 05-13-2020, 04:18 PM - Thread Starter
Senior Member
 
Audiophile75's Avatar
 
Join Date: Feb 2018
Location: The middle of Minnesota
Posts: 369
Mentioned: 13 Post(s)
Tagged: 0 Thread(s)
Quoted: 262 Post(s)
Liked: 238
Subwoofer Room Pressure - spl or freq?

I know SPL stands for Sound Pressure Level but I’m not sure that tells the whole story, or does it? Does frequencies even at low levels come into consideration? I also know a major factor is woofer mass, lots of moving mass, but does that tell the whole story?

Is SPL the same as Room Pressure and at what level / frequency does all this come into play?
Audiophile75 is offline  
Sponsored Links
Advertisement
 
post #2 of 5 Old 05-13-2020, 05:47 PM
AVS Forum Special Member
 
A9X-308's Avatar
 
Join Date: Mar 2008
Location: Australia
Posts: 8,652
Mentioned: 35 Post(s)
Tagged: 0 Thread(s)
Quoted: 1983 Post(s)
Liked: 1699
SPL is determined by the volume displacement (Vd) of air it moves, so basically cone area (Sd) times excursion (Xmax, or x in eqns below) at a given frequency.


Assuming radiation in free space and no directionality, the equation for the sound pressure from a point source can be used:

p=jwQ*rho0/(4*pi*r)

where
w is the angular frequency in rad/s,
Q is the volume flow in m³/s,
rho0 is 1.2 kg/m³,
r is the distance in metres.

The volume flow Q is the derivative of volume, Q=jwV, and volume is displacement*surface V=x*Sd.

All in all this results in

p=-w²*x*Sd*rho0/(4*pi*r)

if x represents the peak value of the displacement, so does p. If it is the RMS value of the displacement, the pressure will also be RMS, and possible to convert to sound pressure level, SPL, in dB by the equation Lp=20*log(|p|/pref), where pref is 20 µPa.



Simplified, if a given driver at a given excursion is producing a given SPL at 80Hz, it will need 4x the Vd at 40Hz and 16 x Vd at 20Hz for the same SPL. The reverse is true as you go up one or two octaves where it will be 1/4 and 1/16th Vd respectively.


This also does not factor in the apparent loudness changes from the Fletcher Munson curves.


Note as the maths above is for free space, ie the enclosure is suspended in free air well above the ground, and the enclosure is small enough that it radiates omnidirectionally, which is basically any dimension is less than 1/4 wavelength at the highest frequency of operation. Put it on the ground and the SPL will increase by 6dB as it's now radiating into 2pi or 1/2 space.


This is all effective for subs, but as you begin to get higher in frequency, the enclosure will become quite large relative to the wavelengths being produced, and directivity will be a factor and change the numbers some, so don't use it there unless you understand.

“You are not special. You are not a beautiful and unique snowflake.” Chuck Palahniuk
A9X-308 is offline  
post #3 of 5 Old 05-13-2020, 11:21 PM
AVS Forum Special Member
 
PrimeTime's Avatar
 
Join Date: Mar 2003
Location: Lower California
Posts: 3,324
Mentioned: 11 Post(s)
Tagged: 0 Thread(s)
Quoted: 836 Post(s)
Liked: 545
SPL has a different significance in a closed chamber than free air. That is, SPL measures pressure, not acoustic power/air volume flow. In a closed system, otherwise known as a pressure vessel, there is no net volume flow, so the ratio of pressure to volume flow is high. This ratio defines the acoustical impedance of the system.

The acoustical impedance in a closed chamber is higher than free air, so for a given pressure (SPL) the power flow (acoustic watt) is much less in a closed chamber than in free air. The higher acoustic impedance (radiation resistance) in a closed chamber is a better impedance match (higher radiation resistance) to an acoustic transducer than radiating into open space. One might say it is the difference between a SPL measurement outside an enclosure and a measurement inside the enclosure.


Horns also perform an impedance-matching function, usually considered in free space.
PrimeTime is offline  
Sponsored Links
Advertisement
 
post #4 of 5 Old 05-14-2020, 04:31 PM
AVS Forum Special Member
 
A9X-308's Avatar
 
Join Date: Mar 2008
Location: Australia
Posts: 8,652
Mentioned: 35 Post(s)
Tagged: 0 Thread(s)
Quoted: 1983 Post(s)
Liked: 1699
A domestic building is not a pressure vessel. It's leaky enough at LF not to build up pressure much and at HF the wavelengths are small enough, and typical in room absorbent material enough that it behaves like free space. The math I posted will get you very, very close to a what a real world measurement will provide.

“You are not special. You are not a beautiful and unique snowflake.” Chuck Palahniuk
A9X-308 is offline  
post #5 of 5 Old 05-16-2020, 12:21 AM
AVS Forum Special Member
 
PrimeTime's Avatar
 
Join Date: Mar 2003
Location: Lower California
Posts: 3,324
Mentioned: 11 Post(s)
Tagged: 0 Thread(s)
Quoted: 836 Post(s)
Liked: 545
A domestic room may not be a perfect pressure vessel, but as a somewhat enclosed space it can possess some of those properties at subwoofer (ULF) frequencies, especially in basements. (A closer example is a crankitup car, even with the flexing steel panels.) Those on the subs ULF forum speak of the ability to "pressurize" a room, which is somewhat necessary to sustain subsonic SPLs. And is one of the reasons why ULF is not practical in larger spaces closer to free air, like cinemas.


The basement home theater may not exhibit the high acoustical impedance of a pressure vessel, but will present a notably higher radiation resistance to a sub than free air.
PrimeTime is offline  
Sponsored Links
Advertisement
 
Reply Audio Theory, Setup, and Chat

Thread Tools
Show Printable Version Show Printable Version
Email this Page Email this Page


Forum Jump: 

Posting Rules  
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are Off
Pingbacks are Off
Refbacks are Off