The inverse square law in rooms? Observations and thought related to power requirements.

[yepimonfire]

The inverse square law states that in the free field, each doubling of distance equates to a loss of 6dB. Rooms are not free field, and the sound that would typically be radiated into space is contained and reflected by the room boundaries.

To determine just how much spl drop applies in a real room, I measured the spl at 1m, 2m, and 4m. According to the inverse square law, I should have experienced a 12dB loss at 4m. At 1m, the spl was 71 dB using band limited pink noise from 500hz-2khz. At 2m, a drop of 3dB occurred, reading 68dB, at 4m, 63dB, or a loss of 5dB from 1m. Increasing the distance beyond 4m (which was about 13’) caused no further loss of spl, however, my room is only 20’ long, so a longer room with more space to the rear wall should continue seeing drops.

When deciding how much power/speaker we need, the peak spl calculator is often referenced, however, this calculator only adds an additional 3dB for room gain, but still follows the inverse square law for increasing distance, therefore, it would estimate that we need much more spl than necessary.

Take my situation for example. The in room sensitivity of my speakers up front is 96dB @1m. I sit 10.5’ away, according to the calculator, this means I lose about 10dB, meaning I’d need about 100w to achieve 105dB Reference level peaks. If we take the real world example I just tested, I actually only lose 5dB, dropping the required power to only about 25w.

My room is fairly well treated too, so others may experience even less of a dB drop. Based on the results of this, I think we should revise calculations for average in room drop.

Is anyone else here with an spl meter willing to test spl drop at 1m and then 2-4m and compare results to the expected 6-12dB loss? I’d be interested in see if this varies significantly by room or even room size.

 

[mtrycrafts]

... I measured the spl at 1m, 2m, and 4m. According to the inverse square law, I should have experienced a 12dB loss at 4m. At 1m, the spl was 71 dB using band limited pink noise from 500hz-2khz. At 2m, a drop of 3dB occurred, reading 68dB, at 4m, 63dB, or a loss of 5dB from 1m. ....

Just a small math quibble.
You lost 5 dB from 2m, for a total of 8 dB instead of 12 in free space.

 

[shadyJ]

The inverse square law states that in the free field, each doubling of distance equates to a loss of 6dB. Rooms are not free field, and the sound that would typically be radiated into space is contained and reflected by the room boundaries.

To determine just how much spl drop applies in a real room, I measured the spl at 1m, 2m, and 4m. According to the inverse square law, I should have experienced a 12dB loss at 4m. At 1m, the spl was 71 dB using band limited pink noise from 500hz-2khz. At 2m, a drop of 3dB occurred, reading 68dB, at 4m, 63dB, or a loss of 5dB from 1m. Increasing the distance beyond 4m (which was about 13’) caused no further loss of spl, however, my room is only 20’ long, so a longer room with more space to the rear wall should continue seeing drops.

When deciding how much power/speaker we need, the peak spl calculator is often referenced, however, this calculator only adds an additional 3dB for room gain, but still follows the inverse square law for increasing distance, therefore, it would estimate that we need much more spl than necessary.

Take my situation for example. The in room sensitivity of my speakers up front is 96dB @1m. I sit 10.5’ away, according to the calculator, this means I lose about 10dB, meaning I’d need about 100w to achieve 105dB Reference level peaks. If we take the real world example I just tested, I actually only lose 5dB, dropping the required power to only about 25w.

My room is fairly well treated too, so others may experience even less of a dB drop. Based on the results of this, I think we should revise calculations for average in room drop.

Is anyone else here with an spl meter willing to test spl drop at 1m and then 2-4m and compare results to the expected 6-12dB loss? I’d be interested in see if this varies significantly by room or even room size.

What kind of test signal are you using? Different speakers will have different loss rates with distance, and frequency can also be a factor, as well as the axis that you are measuring on. The speakers I am using right now are fascinating in this regard. Something else to keep in mind is the rate of fall off with distance can also change with distance (and frequency). For example, line-arrays will fall off at a 3 dB per doubling of distance, but only up to a certain distance, and then will start to fall off at a 6 dB per doubling of distance. Only a true point source will fall off at a 6 dB per doubling of distance, but no speaker is a true point source design. Most conventional speakers sort of emulate point source sound emission, and some come close. The air itself also attenuates sound with frequency as a factor, and this can change with humidity, air pressure, and temperature.

 

[yepimonfire]

Just a small math quibble.
You lost 5 dB from 2m, for a total of 8 dB instead of 12 in free space.

Must not have worded the post clearly

I lost 5dB TOTAL, so the reading went from 70dB to 65dB at 4m, 3dB at 2m, or 70dB to 67dB.

 

[yepimonfire]

What kind of test signal are you using? Different speakers will have different loss rates with distance, and frequency can also be a factor, as well as the axis that you are measuring on. The speakers I am using right now are fascinating in this regard. Something else to keep in mind is the rate of fall off with distance can also change with distance (and frequency). For example, line-arrays will fall off at a 3 dB per doubling of distance, but only up to a certain distance, and then will start to fall off at a 6 dB per doubling of distance. Only a true point source will fall off at a 6 dB per doubling of distance, but no speaker is a true point source design. Most conventional speakers sort of emulate point source sound emission, and some come close. The air itself also attenuates sound with frequency as a factor, and this can change with humidity, air pressure, and temperature.

Technically it still shouldn’t matter in a room, even if we had a true point source with 360 degree radiation at all frequencies, that sound would just bounce off the front and side walls and floor/ceiling and be still be contained in the room anyways. I used 500-2000hz PN as a signal, that way I avoided skewed results due to standing waves and HF attenuation. I don’t think HF attenuation at short distances in rooms is that big of a problem. Even at 20khz, in a 72 degree room with 50% humidity in a big room, seated 15’ away, you only lose 2dB. At 12khz, it’s only 1dB lost at 15’.

 

[MrBoat]

In all the places I have lived in the last 40 years, not one living room needed more than 120w. Systems rated at around 100w averaged running at about half of their maximum for what is considered relatively high SPL, or, NIL (Neighbor Irritating Levels).

My room is 12' X 20' and my Denon AVR is rated at 120wpc into 8 ohms. With the Fusion-12's, I am barely flexing them or the amp before I give up, without any point in this room, or any of the other attached rooms offering much, if any escape, even when putting a door between.

I've always just used 100wpc as a safe minimum regardless of the speakers, for anything beyond apartment living.

 

[mtrycrafts]

In all the places I have lived in the last 40 years, not one living room needed more than 120w. Systems rated at around 100w averaged running at about half of their maximum for what is considered relatively high SPL, or, NIL (Neighbor Irritating Levels).

My room is 12' X 20' and my Denon AVR is rated at 120wpc into 8 ohms. With the Fusion-12's, I am barely flexing them or the amp before I give up, without any point in this room, or any of the other attached rooms offering much, if any escape, even when putting a door between.

I've always just used 100wpc as a safe minimum regardless of the speakers, for anything beyond apartment living.

The only speaker that needs much more are subs, way more.
I see over 200W on each of two subs on a number of hard hitting passages.

And, I rarely see 15W on my center.

 

[MrBoat]

The only speaker that needs much more are subs, way more.
I see over 200W on each of two subs on a number of hard hitting passages.

And, I rarely see 15W on my center.

Subs, I agree. Weird though, that the old 3 ways that could reach below 40hz with authority with a lot less power. Granted, now there is LFE content with HT in the mix. So then, it's the HT faction that is robbing all the efficiency from our systems.

 

[everettT]

Seems like more listening, less theory would be a good place to start. After that serious measurements and understanding them would be next.