# Max SPL calculation?

Status
This old topic is closed. If you want to reopen this topic, contact a moderator using the "Report Post" button.

#### Ignite

This eludes me... There doesn't seem to be information anywhere on this. How does one calculate max SPL given wattage and driver sensitivity? Also how does one calculate theoretical excursion at a given frequency and power?

#### Freddie

If I remember this correctly, each time you double the amplifier power you'll get a 3dB increasement.

So If you have a driver with 90dB/W sensitivity, it means that with 1 W you will will get 90dB. With 2W 93dB, with 4W 96dB, 8W 99dB, 16W 102dB, 32W 105dB.... So If you are want to play really loud, go for drivers with high sensitivity. It will probably be a lot cheaper than buying a bigger, more powerfull amp.

/Freddie

#### f4ier

.... and here how to estimate Xmax given SPL, Sd and frequency.

Xmax = (0.00118*pi*(10^(SPL/20))) / (Sd*f*f)

where:
pi = 3.1415926535897932384626433832795
SPL in dB
Sd in square meters
f in frequency
Xmax in mm

Isaac

#### AndrewJ

f4ier has the correct equation for calculating excursion, but I would just like to point out some additional qualifications to the units. SPL is the rms value, in dB, even though excursion is given in peak value,and these calculations are based on the SPL in 2pi (or half) space, not 4pi. You would need twice this excursion to gennerate the same SPL in free field.

#### exuviae

So

Ok i am a bit slow, is there some calculation given an amount of watts and sensitivty that tells you a theoretical max spl? For example I have SoundStream Tarantual series T4-15 with a 91db at 1 watt at 1 meter, and will be pushing those with a 2000 watt rm Picasso PCA200D amp also from soundstream. Without sitting there figuring out exponents (2, 4, 8, 16, 32, 64, 128,256,512,1024,2048) i know this because of computer programming lol. By your calculations i would only hit around 124db. I think that is right, 11 double in power, 3db gain for a total gain of 33db added to a sensitivity of 91db = 124. However on 1000 watts and 2 10" in a ported box i hit 138.9 on a term lab meter (official meter of db drags) and the box was to small for the speakers, and the starting sensitivity was only 82. Something just don't add up, with 2 15"'s seeing 2000 watts i should be in the 145-150 on the term-lab meters.

#### noodle_snacks

sensitivity + 10log(power)

eg

91 + 10log(2000) =124.0103

#### AudioFreak

If we are talking SPL drags then we are talking inside the cabin of a car. You'll have cabin gain amongst other things.

#### AndrewT

Hi,
are we really talking about 25db to 27db of cabin gain?

#### noodle_snacks

In my experiance cabin gain is maybe 4db/oct from 80hz or lower depending on the size of the car, you only get that sort of gain at very low frequencies. I do think the car this was for had a leeky boot though.

#### AndrewT

f4ier said:
.... and here how to estimate Xmax given SPL, Sd and frequency.

Xmax = (0.00118*pi*(10^(SPL/20))) / (Sd*f*f)

where:
pi = 3.1415926535897932384626433832795
SPL in dB
Sd in square meters
f in frequency
Xmax in mm
Hi,
I have a dual driver vented cabinet.
How do I use the Xmax formula?
Calculate for one driver using SPL-6db? or something else?

How do I take account of the boost/gain around the port frequency?

#### Drew Eckhardt

Re: Spl

soufiej said:
Could this possibly be what you need; http://www.myhometheater.homestead.com/splcalculator.html

This takes into account the number of speaker enclosures in the room and room gain.

While it takes into account the boost from placement near boundaries, it completely disregards the room's reverberant characteristics and speaker directivity.

With direct radiating speakers in typical rooms the SPL is greater at the listening position (whether 5, 10, or 20' away) than what you predict at 1 meter on-axis.

#### AndrewT

Hi Drew,
it's not the room I'm chasing, but the driver.
Thanks for looking that up.

#### Svante

The maximium output level (MOL) of a closed box system is mainly limited by two factors; cone excursion and maximum power dissipation in the voice coil. The excursion limit dominates for low frequencies.

For a bass-reflex system MOL is increased around the Helmholtz resonance, but another limit is also introduced due to port overloading.

The limits are all frequency dependent.

The resulting MOL is dependent on frequency and is rather complicated to calculate by hand. It ends up something like this (for a bass-reflex system) (gray curve)

An externally hosted image should be here but it was not working when we last tested it.

#### AndrewT

Hi Svante,
I see the four regions in the basta curve.

1.) The nearly flat on the right.
2.) the dip where Xmax limit sets in.
3.) the slope just to the left of the dip.
4.) the roll off at the extreme left.

Can I presume that the Xmax from SPL formula applies to region 3?

If it does, then how do I use it when two drivers are mounted in the box?

#### Svante

AndrewT said:
Hi Svante,
I see the four regions in the basta curve.

1.) The nearly flat on the right.
2.) the dip where Xmax limit sets in.
3.) the slope just to the left of the dip.
4.) the roll off at the extreme left.

Can I presume that the Xmax from SPL formula applies to region 3?

If it does, then how do I use it when two drivers are mounted in the box?

No, Xmax limits in regions 2 and 4. In region 3 the vent limits MOL. I am not sure which formula you are referring to, but almost certainly it is only valid for region 2 (not 4). Most probably it is intended for closed boxes (and this was a bass-reflex box).

Here are the limits that are used to calculate MOL in Basta!

An externally hosted image should be here but it was not working when we last tested it.

You can look more closely at how it works in the user's guide:

http://www.tolvan.com/basta/Basta!UsersGuide.htm

#### AndrewT

Hi Svante,
the formula in post3
Xmax = (0.00118*pi*(10^(SPL/20))) / (Sd*f*f)
would show a continually falling SPL as frequency drops.
I would think that prediction is correct for the one driver.
The reference you pointed to, shows region 3 with a minima with rising maximum SPL either side of the minimum (not clearly visible in the posted graph).
You are surely referring to some other formula, unfortunately I could not find the formulae in the Basta site.

So I come back to my original question? How do I adapt the graph or formula to take account of two drivers in the cabinet?

#### Svante

AndrewT said:
Hi Svante,
the formula in post3 would show a continually falling SPL as frequency drops.
I would think that prediction is correct for the one driver.
The reference you pointed to, shows region 3 with a minima with rising maximum SPL either side of the minimum (not clearly visible in the posted graph).
You are surely referring to some other formula, unfortunately I could not find the formulae in the Basta site.

So I come back to my original question? How do I adapt the graph or formula to take account of two drivers in the cabinet?

Ok, so there is no single formula in Basta!, the response is rather calculated by simulating a rather complicated network of mechanical and electrical components.

This is partially my point, equations work for simple model cases, but in real life several things limit MOL. To get a grasp on the behaviour of a system over the entire frequency range it is best to simulate it.

The formula you mention is probably for closed boxes, and they don't behave like the bass-reflex box. For the closed box, the MOL will drop proportional to 1/f*f just as in your equation. For the bass reflex, the curve becomes bent because of the support from the vent.

If you have two drivers, Sd is doubled. This in turn leads to + 6 dB in MOL (as limited by Xmax).

Status
This old topic is closed. If you want to reopen this topic, contact a moderator using the "Report Post" button.