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
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)
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.
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)
I believe you've done a very good job of capturing the essentials.

On this Daedalus Audio webpage, there is a link titled ".....more...(reprint on loudspeaker sensitivity from Musical Fidelity)."

It has some very helpful information along the lines being discussed here, IMO.
Thanks for the advice Shadorne. It was useful and much appreciated. Regarding listening to LOUD music up to 100dB SPL or higher, I have measured the SPLs from 4 meters away at the listening position using a Radio Shack SPL meter and the needle has never gone past 90dB in the peaks during fluctuations when listening at insane volume levels. In fact the maximum SPL I have got when listening to very loud music is 88dB in the peaks as my ears often give up first before something blows up in flames of fire. In this sense I am little amazed when reading about folks listening up to 100dB or beyond that. Maybe my ears are less tolerant compared to others with stronger immunity to high SPLs. My average SPLs are around 70-80dB when listening to reasonably loud music.

Yes, I am well aware that Harbeths are not designed to play at high SPLs and as such have practiced caution as to prevent any excessive over-driving to these delicate speakers. The perception of loudness varies with different individuals as I personally find the Harbeths are able to cope up with my expectations when I crank up the volume and blast the music. Most often my ears give up first(90dB peaks) before my speakers(or ear drums) blow up. My amp is rated at 80W so I guess I have got everything covered in my listening habits. By the way, the listening position is not against the wall as there is a 3' space from the chair to the back wall. I do know the effects of placing the chair directly against the wall and I don't like the results either.
Thanks for the link Tvad. I have gone through the document and it seems to make more sense now. I particularly agree with the statement that loudspeaker sensitivity ratings are often overstated by a few dBs. That is the reason it is always prudent to practice extra caution by allowing some buffer to account for all these anomalies by means of listening at lower volumes several notches below the ultimate output of the amplifier, or by getting a substantially higher-powered amp.
Power isn't everything. 30 watts from a Pass Labs may be sound louder than 60 watts from a cheap yamaha receiver. It's quality vs quantity.

Keep in mind that your 80 watts will be hard to beat without going to a massive amp. 80 watts to 160 will only gain you 3db. To double the perceived volume you need to increase by 10db. In other words, you need to get to 200+wpc to really hear a difference with a similar quality amp.

My final input with your calculations is placing speakers against walls or in corners to gain bass volume/db. No 2 speakers will gain the same benefits or problems by moving them closer to a wall. Almost every time though, you will lose a lot of imaging by doing this and probably get "boomy" bass.
Yes, I forgot to mention about quality power between a good amp and a cheap receiver. The same goes with power differences between solid-state and tube amps. Both my Plinius and Rega amps rated at 100W and 80W respectively sound much louder than my top model Sony 5-channel amp AV rated at 130W. Not only that, using the BTL function of the Sony amp can increase the power from 130W to about 210W in 2-channel mode. Even at this power output the Sony amp sounds substantially "weaker" than both my 2-channel audiophile amps. Until now I don't have any clue to explain this in a technical perspective although price-wise the cheap Sony is taken for granted to sound softer. Due to this experience I have lost respect in the Sony brand in coming up with inferior mass-market amps although they seem do much better in other areas.

Another issue I read for years is tube amps sound substantially more powerful than a solid-state amp with both having similar power ratings ie. a 20W tube amp can sound much more powerful and louder than a similar 20W solid-state amp, or an 8W tube amp sounds more powerful than a 30W SS amp. Yet again I don't know how to explain this phenomenon. It would be good if someone with technical knowledge and experience can clarify.
In fact the maximum SPL I have got when listening to very loud music is 88dB in the peaks as my ears often give up first before something blows up in flames of fire.

At 4 meters this requires 88 + 12 = 100 db SPL from the speakers. From the amp this requires 32 watts. So you should be easily OK to reach these peak level without any problems of any sort from your amp or speakers.
"09-26-09: Ryder
Thanks for the advice Shadorne. It was useful and much appreciated. Regarding listening to LOUD music up to 100dB SPL or higher, I have measured the SPLs from 4 meters away at the listening position using a Radio Shack SPL meter and the needle has never gone past 90dB in the peaks during fluctuations when listening at insane volume levels. In fact the maximum SPL I have got when listening to very loud music is 88dB in the peaks as my ears often give up first before something blows up in flames of fire. In this sense I am little amazed when reading about folks listening up to 100dB or beyond that. Maybe my ears are less tolerant compared to others with stronger immunity to high SPLs. My average SPLs are around 70-80dB when listening to reasonably loud music."

This is due to a very skewed freq response, meaning one that is bass anemic.
Ryder, have you ever measured your in room freq response?
It is easy to do and will ultimatly help you get great sound from your speakers.
Also it will help you in selecting appropriate amplification.

Bob
09-26-09: Ryder
...the maximum SPL I have got when listening to very loud music is 88dB in the peaks as my ears often give up first before something blows up in flames of fire...My average SPLs are around 70-80dB when listening to reasonably loud music.

Everyone has his own definition of "loud", but these readings are pretty low, and I wonder if there's a glitch in the measuring method.

Do you have your Radio Shack decibel meter set to "C" weighting, and "Fast" response when taking your measurements? If not, consider changing to these settings and then testing again.
Bob, I have not measured the in-room frequency response of the room since I am quite happy with the sound I'm currently getting from the speakers. Furthermore there isn't much allowance to move the speakers around and I have no plans to add EQ correction or a sub to the system. Nevertheless I will do a measurement someday and see how flat the frequency curve would be.

Yes, I have the Radio Shack SPL meter set to "C" weighting and "Fast" response when the measurements were taken. I am 100% positive it's my ears and nothing else. I have sensitive ears and suffer from mild hyperacusis hence cannot tolerate very high SPLs. My problem started during my younger days when I listened to very loud music(probably >90dB) and my hearing might have been damaged during that time. Since the symptoms have somehow diminished these recent years, I am trying to preserve my hearing by listening at low to moderate volume nowadays although I occasionally still crank up the music. I have to admit my ears are not as strong compared to a few others.
Ryder, thanks for the explanation. I was just checking...
Ah, that explains it better.
I often suspect that some who are not familiar with undistorted loud volume sound subconciously go into defensive mode in anticipation of pending distortion. To avoid distortion it helps to have plenty of clean headroom. Any one who attends live classical concerts and has sat fairly close to the stage can attest to the just how loud the music can become.
This is all done for one speaker (unless I missed that point. In that case: sorry!). Since most of use two speakers in the room, what does that mean? I seem to recall that you can add 3 dB (A) to the equation.

As for quality/quantitiy: 1 Watt is 1 Watt, from whatever amp it comes. Whether or not it will sound as good... that's an other debate.
Hi Ryder, I just looked at your system page and noticed all of the room treatment including the diffusion. Well done!
If you are interested in measuring your in room response, I would recommend the free program REW )Room EQ Wizard which is available for free at the Home Theater Shack. Besides freq response it also measures RT60 times and does waterfall plots and a few other nice features. Let us know when you do it and then you can post a graph here. I am sure it will be superb!

Bob
Satch, re: Watt quality; yes, no one is arguing the criterion of the measurement, it's about what sounds better. I, perhaps incorrectly, assumed that would be understood.
Only 1 fly in the ointment.

If you need say .... 100 watts to produce the desired SPL, there is another factor to consider.
IF the speaker presents a bad load to the amp, in the sense of large phase angle, you can cut in to available power badly. If you need a calculated 100 watts and the speaker is 45' phase angle, you really need 141 watts to deliver 100 watts.
Large phase angle and low impedance at same or near-same frequency is a deal breaker for many amps.
I simply don't know where to draw the line. Are 'cheap' good watts really cheaper than a speaker with a more moderate load? Can you find a speaker you enjoy that has easier electrical characteristics?
I'd personally be willing to try a solution with a smaller amp than my ICE amp of 250/side and more sensitive speakers than my panels....though electrically, they are not as bad as most.
Magfan, that's certainly a plan. FWIW, and with all due respect to those who feel that they've succeeded with that approach, I've yet to hear high sensitivity speakers that are more compelling than less sensitive speakers across all the paramters that I seem to find important.
Un:
Also FWIW, it seems that people rely on 'cheap watts' to make up for some pretty wild speaker designs.
Also, most opin that it is impedance (low) which makes for a bad speaker load.
That is simply not true. Even an 8ohm near-resistive speaker (ideal imp?) would be a monster if the phase angle were say.... 60' or more across a wide portion of the hi energy frequency range.
This is speaking purely electrically. I don't know how good hi sensitivity speakers sound. It is possible that since I am accustomed to panels I too may find this unacceptable.
I'm not gonna touch tube vs SS or Voltage vs Current source amps. All have there best use.

Try this if you are curious::

http://www.hometheaterhifi.com/component/content/article/228.html

This is a good graphic and a very good way to 'visualize' true speaker goodnes, at least electrically.
Interesting link, thanks.

09-26-09: Shadorne
At 4 meters this requires 88 + 12 = 100 db SPL from the speakers. From the amp this requires 32 watts. So you should be easily OK to reach these peak level without any problems of any sort from your amp or speakers.
Shadorne, there has been some changes. The peak SPL I am getting when listening at insane volume levels has increased to 96dB. My listening distance is now 3.5m(front plane of speakers to the ear). I have run a quick calculation. At 3.5m listening distance there would be an additional 10.5dB. The speaker would be producing 96 + 10.5 = 106.5dB at 3.5 meters away.

I have rechecked the specifications of my integrated. The power output is rated at 82W into 8 ohms and 127W into 4 ohms. My question is do we always take the figure going into 8 ohms although the impedance on the speaker will always be fluctuating from probably 4 to 8 ohms? An 82W amp(8 ohms) is only capable of 104.84dB, and the peak SPL of 106.5dB I am getting has slightly exceeded the maximum output of the amp. I reckon I am getting a slight distortion in the music listening at these levels.

Power output of amplifier at increasing SPL
1W @ 86dB
2W @ 89dB
4W @ 92dB
8W @ 95dB
16W @ 98dB
32W @ 101dB
64W @ 104dB
82W @ 104.84dB (extrapolated)
128W @ 107dB

I guess my amp may be working at borderline at a peak SPL of 106.5dB. This is only on the amplifier. I am not sure whether the speakers can handle this peak SPL or not. I need to check with the designer before I overstress the woofers.

Thanks in advance.
The designer for Harbeth, Alan Shaw cannot factually answer the question of the maximum SPL the speakers can handle and has advocated good listening habits in respecting our ears. Harbeth speakers were said to have been designed to sound warm and natural at moderate volume levels.

As such, I have rearranged my listening position to be 3 meters away from the speakers. The reduced listening distance has brought down the peak SPL to about 93dB. With this arrangement the additional 9dB from speakers would produce 93 + 9 = 102dB at 3 meters away.

I'm covered now on both the amplifier and speaker end(I think the 8" driver of the SHL5 must be able to handle up to 102dB since the max SPL of the ATC SCM7 with 5" driver is up to 103dB).

No more issues.
I think the 8" driver of the SHL5 must be able to handle up to 102dB since the max SPL

I would be pretty sure it can handle that SPL at 1 meter. My guess is that the max speaker output will be around 105 db SPL at 1 meter (with still some headroom for transients at certain frequencies).

If 96 db spl at the listening position sounds insanely loud then you probably are getting distortion at that level.