Ramtubes 11-27-2018:
Thanks for your measurements and math. I think the math will leave most with their head swimming. Perhaps you could add some details to the steps so that others, less math inclined, might work things out. it is nice for people to know how different speakers fall off with distance. Perhaps you could write that up for us. :)
I ask for SPL both at listening position and 1 meter for two different purposes.
I want to get to know the listener and measuring at 1 meter leaves out all those other calculations. One just works off the 1 meter speaker spec and adds or subtracts. If one is 3 db higher than the speaker spec he is at 2 watts, 6 db is 4 watts, 10 db is 10 watts, 20 db is 100 watts.
Thanks for your comments about my post, Roger.
I guess the first thing I should emphasize is that the dynamic ranges of the two recordings I referred to in my previous post, while being applicable to MY determination of minimum required amplifier power, are VASTLY greater than the dynamic ranges of most or all of the recordings most others listen to. And in fact are much greater than the dynamic ranges of most of the recordings I listen to. So my bottom line of a 32 watt minimum power capability, for my purposes, is likely to be considerably less for those who listen at comparable average volume levels (average SPLs say in the 70s at the listening position) **if comparably efficient speakers are used.**
This is consistent, btw, with statements I believe Roger made earlier in the thread to the effect that many listeners require less power than they tend to believe.
I’ll also say that the point to going through the kind of calculations I described in my previous post is of course NOT to make any kind of final determination of what amp to choose, which of course should be made by listening, assuming that is possible. The point is to narrow the field of candidates that are to be considered, and to minimize the likelihood of making an expensive mistake, that would perhaps work for some of the listener’s recordings (especially those having narrow dynamic range), but would not work (or at least would not work well) for other recordings (especially those having wide dynamic range).
Another important point to keep in mind is that speaker sensitivities are often specified as the SPL produced at 1 meter in response to an input of 2.83 volts, rather than 1 watt. For an 8 ohm speaker (that is truly 8 ohms) 2.83 volts corresponds to 1 watt, so the two kinds of specifications will be identical. But 2.83 volts into 4 ohms corresponds to 2 watts, so for example a 90 db/2.83 volt/1 meter/4 ohm speaker is really just an 87 db/1 watt/1 meter/4 ohm speaker.
Regarding measurements at 1 meter, I haven’t done that (aside from during the unique speaker calibration processes that are required to utilize the capabilities of my DEQX HDP-5), mainly because it wasn’t necessary for my purposes, and because at least in my case making the determination from the listening position and performing the necessary calculations isn’t difficult. Also, while 1 meter measurements would simplify the calculations somewhat, as Roger mentioned, one would still have to somehow address the effects on SPL of having two speakers, as well as addressing room effects in some manner.
... it is nice for people to know how different speakers fall off with distance. Perhaps you could write that up for us. :)
In general the SPL provided by a box-type dynamic speaker (meaning a speaker that is non-planar and is not a line source) will fall off at 6 db per doubling of distance, **neglecting the effects of room reflections.** (As can be seen in my previous post, I added 3 db to my calculations as a rough guess of "room gain" as perceived at the listening position). The fall-off of planar and line source speakers as distance increases will be significantly less than that, as those speakers tend to throw their sound forward. The reason being, I believe, that as listening distance increases the angle between the listener’s ears and central part of the speaker and the upper part and the lower part of planar and line source speakers decreases to a greater degree (pun intended) than in the case of typical dynamic speakers having drivers that are spaced relatively closely. Making the sound emitted by those parts of planar or line source speakers more able to contribute to the perceived SPL than at smaller distances.
A fall-off of 6 db per doubling of distance can be extrapolated to any combination of distances based on the formula 20 x log(D1/D2), where “log” is the base 10 logarithm. If D1 is greater than D2 the answer will be a positive number; if D1 is less than D2 the answer will be the same number except with a minus sign in front of it. One can perform this calculation with a scientific calculator, or with the calculator that is built into Windows if it is set to scientific mode, or with various online calculators. In my case my listening distance is 12 feet. 12 feet is 144 inches; 1 meter is 39.37 inches; 144/39.37 = 3.66 meters. 20 x log(3.66/1) = 11 db, rounded off. So the SPL produced by a single box-type dynamic speaker at 12 feet will be about 11 db less than at 1 meter, neglecting room effects.
The conversion of dbW to watts that I showed in my previous post is based on the ratio of two power levels, expressed in db, being 10 x log(P1/P2), where “log” is again the base 10 logarithm. If P1 is greater than P2 the answer will be a positive number; if P1 is less than P2 the answer will be the same number except with a minus sign in front of it. So it can be calculated that 32 watts is 10 x log(32/1) = 15 db greater than 1 watt, which can be expressed as 15 dbW. Converting in the opposite direction (15 dbW to 32 watts) is a bit trickier mathematically, but no doubt there are online calculators which can facilitate that.
Best regards,
-- Al
