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Amplifier Power Ratings & Speaker Sensitivity

We often hear comments about amplifier X does not have sufficient power to drive speaker Y or speaker Z requires minimum 200W to come alive. I am trying to figure out if there is a correlation between amplifier power ratings and speaker sensitivity in the prevention of over-driving of speakers when listening at high volume levels since stressing an amplifier beyond its intended output will cause the amp to clip that may subsequently cause damage to the coils of the speaker.

From what I have read, below is my understanding but please correct me if any of my interpretations are wrong.

1) For a manufacturer's stated sensitivity of say 86dB/W/m, 1W of power is required to produce 86dB SPL at a distance of 1m away from the drivers.

2) In the doubling of power, the SPL will increase by 3dB. For example :-
1W @ 86dB
2W @ 89dB
4W @ 92dB
8W @ 95dB
16W @ 98dB

3) For every distance added, the SPL will decrease by 6dB. For example :-
86dB @ 1m
80dB @ 2m
74dB @ 3m
68dB @ 4m
62dB @ 5m

4) Close placement to rear wall will boost 3dB in the bass

5) Close placement to a corner will boost 6dB in the bass

To determine whether an amplifier is capable of driving the speakers at a given loudness and distance without causing damage to either the speakers and/or the amp, can we use the power rating of the amp and the sensitivity of speakers as a basis in controlling the level of loudness we are getting from the system? Let say a 50W amp is used to drive a speaker with 86dB sensitivity and the listening distance is approximately 4 meters away. Can we work backwards from the peaks we are getting in the SPLs from the listening position? With the assumption of 90dB as the absolute peak SPL when listening at insane volume levels at 4 meters away(-18dB){at least in my case although I am aware some folks listen past 100dB}, the SPL at 1m away is 72dB.

At 4 meters listening distance,
1W @ 72dB
2W @ 75dB
4W @ 78dB
8W @ 81dB
16W @ 85dB
32W @ 88dB
64W @ 91dB

64W of power is required to produce 91dB SPL. If using lesser powered amplifiers of 60W and below, the amp will have potential to go into clipping. If listening at 88dB SPLs(peaks) and lower there would not be any concern on speaker or amplfier damage.

I do know that room conditions, amplifier gain, power supply and some other factors will play a part as well but the above should at least give a basic idea by providing a rough estimate on how loud should one be listening so as to prevent any damage to the components?

I understand that people with high-powered amps will not need to worry so much when cranking up the volume but it can be useful for some other folks who have flea-powered amps(especially tube amps), particularly those who like to listen loud.

Any advice or feedback would be most appreciated.
ryder
shadorne's avatar
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shadorne
7,477 posts
 
Your back of the envelope calculations are roughly correct.
However, for every DOUBLE of the distance, the SPL will decrease by 6dB. Remember that 91 db SPL peak is hardly loud at all. Average at 91 db SPL with peaks at 100 db SPL is only beginnig to get really loud. Most concerts sound great to fans and they play at up to 105 db SPL average for many of the punchy numbers.

The problem with your position (4 meters back) is that an 86 db SPL sensitivity speaker is going be required to play at 112 db SPL to get you those 100 db SPL peaks (that your speaker can even do this without huge amounts of distortion is extremely unlikely for 99% of speakers). It also means your amplifier needs to belt out 512 watts on those peaks - which 99% of amps cannot do.

So what does this mean - in practice once you get to around peak levels of 91 db SPL (lets assume 85 db SPL average) then you start to hear distortion and PERCEPTIVELY everything begins to sound extremely and dangerously loud 0 although in actual fact it isn't at all (it is just you are starting to get lots of distortion)
shadorne's avatar
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shadorne
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FWIW - I looked at your setup and the living room is a lot of space for those little speakers to fill. Harbeths are awesome but that is definitely a near-field type speaker it is not designed for such a large space unless you listen only at quite modest levels. Something like a B&W 801 with a couple of Bryston 7B's might alter your opinion on how loud you like it - but the small compact Harbeth's don't have a hope to get anywhere near realistic loud in that huge space at such a distance.
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shadorne
7,477 posts
 
One other point I noticed - your listening position appears to be against a wall. This is rather bad news and it will also affect how cluttered and claustrophobic the sound field is perceived at higher levels. You definitely need space behind your head to separate out the reflections from the primary signal. (Sorry I shoudl have combined all these thoughts in one post - BTW you have a stunning home - absolutely beautiful)
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