frequency vs power graph?

[kenshone]

Newbish question: say you have a full-range driver. Is there is a formula that would approximate the power required to generate a sound at a fixed dB?

For example, with frequency on the x-axis and watts on the y-axis, would the graph have a shape similar to that of y = 1/x but shifted? Or y = -x?

If any hopefully realistic assumptions need to be made to answer the question, can you also let us know what those are?

 

[thulle]

With the usual slightly increasing sensitivity in higher frequencies you'd need lower voltage, and with higher impedance in higher frequency the same voltage would result in lower amperage. Lower voltage and current = less power for same SPL at higher frequencies. But I'm not sure there's any good approximation, and you have an impedance bump at lower frequencies around the resonant frequency of the driver, and sensitivity drops off too, so even if you get a good approximation for the upper frequencies it starts to break down at the lower ones.

 

[voodooless]

The sensitivity figure, combined with the frequency response and impedance gives you what you need. Since a speaker ideally has a flat response, it needs the same voltage at every frequency. Hower impedance is not flat, so while voltage might be the same, the current is not. The sensitivity tells you how much dB you get for a certain voltage or wattage (depending on definition). From there it's just extrapolating: double the power for every 3 dB added.

What is the point of your question exactly?

 

[kenshone]

I'm trying to estimate the optimal power requirements of a HT system I'm setting up. I can consider the impedance curves, sensitivities, and max clean output of various amps and speakers.

 

[voodooless]

I'm trying to estimate the optimal power requirements of a HT system I'm setting up. I can consider the impedance curves, sensitivities, and max clean output of various amps and speakers.

Use something like this: http://www.hometheaterengineering.com/splcalculator.html

 

[xaviescacs]

This is purely mathematical, not based on audio knowledge. y = 1/x has a strong discontinuity at x = 0 and too steep around that, perhaps a negative exponential with x >= 0 is better, namely y = a*e^(-b*x) where a controls the value of y at x = 0, and b the steepness of the curve.

 

[DonH56]

Newbish question: say you have a full-range driver. Is there is a formula that would approximate the power required to generate a sound at a fixed dB?

For example, with frequency on the x-axis and watts on the y-axis, would the graph have a shape similar to that of y = 1/x but shifted? Or y = -x?

If any hopefully realistic assumptions need to be made to answer the question, can you also let us know what those are?

The SPL fall-off with distance depends upon your speakers and room, usually in the 3~6 dB loss range for each doubling in distance. A speaker with 96 dB/W/m sensitivity will produce roughly 90~93 dB at 2 m, 87~90 dB at 4 m, and so forth. The previously-referenced SPL calculator (http://www.hometheaterengineering.com/splcalculator.html) provides a rough estimate of the power needed. I generally just estimate using the nominal impedance and sensitivity ratings from the manufacturer and/or reviews.

Be sure to notice the loudness comparison chart; 80 dB average is very loud to me, so I listen around perhaps 70 dB average. IME most people's average listening power is much less than they think, while the peak power relative to that average is higher than they think. For example, in a recent conversation a friend was convinced he used 25~50 W on average and needed 100~200 W for peaks (about 6 dB headroom). In fact he was using 1~2 W on average but needed 50~100 W for peaks (17 dB headroom). The change in dB for power is dB = 10*log10(P2/P1).

For reference:
+1 dB change in volume is barely noticeable and requires 1.26x the power
+3 dB increase is what most of us do when asked to "turn it up just a little" and requires 2x (twice) the power
+6 dB increase is a (very) noticeable increase and requires 4x the power
+10 dB sounds about twice as loud and requires 10x the power

Having 17 dB headroom (50x power) for music and perhaps 20 dB (100x power) for movies will cover most any situation. Some movies have even higher ratios, but frankly I am not too worried about a bit of clipping on a gun shot or explosion.

HTH - Don

 

[DVDdoug]

with frequency on the x-axis and watts on the y-axis,

If you have a frequency response graph for your speakers it has frequency on the X-axis and decibels on the Y-axis.

Then you can use the speaker's sensitivity rating (usually dB SPL at 1W and 1 Meter) to add/change the Y-axis to Watts. It's the same graph with different numbers. (It will be logarithmic unless you re-draw it.)

As you change the volume (Wattage) the graph just moves up or down while retaining the same shape (until you drive the speaker into distortion).

 

[kenshone]

The SPL fall-off with distance depends upon your speakers and room, usually in the 3~6 dB loss range for each doubling in distance. A speaker with 96 dB/W/m sensitivity will produce roughly 90~93 dB at 2 m, 87~90 dB at 4 m, and so forth. The previously-referenced SPL calculator (http://www.hometheaterengineering.com/splcalculator.html) provides a rough estimate of the power needed. I generally just estimate using the nominal impedance and sensitivity ratings from the manufacturer and/or reviews.

Be sure to notice the loudness comparison chart; 80 dB average is very loud to me, so I listen around perhaps 70 dB average. IME most people's average listening power is much less than they think, while the peak power relative to that average is higher than they think. For example, in a recent conversation a friend was convinced he used 25~50 W on average and needed 100~200 W for peaks (about 6 dB headroom). In fact he was using 1~2 W on average but needed 50~100 W for peaks (17 dB headroom). The change in dB for power is dB = 10*log10(P2/P1).

For reference:
+1 dB change in volume is barely noticeable and requires 1.26x the power
+3 dB increase is what most of us do when asked to "turn it up just a little" and requires 2x (twice) the power
+6 dB increase is a (very) noticeable increase and requires 4x the power
+10 dB sounds about twice as loud and requires 10x the power

Having 17 dB headroom (50x power) for music and perhaps 20 dB (100x power) for movies will cover most any situation. Some movies have even higher ratios, but frankly I am not too worried about a bit of clipping on a gun shot or explosion.

HTH - Don

Thanks Don. Is speaker impedance accounted for within all the factors you've listed?

 

[DonH56]

Thanks Don. Is speaker impedance accounted for within all the factors you've listed?

As I said, I normally just use the nominal impedance. Trying to account for impedance over frequency is challenging (you'd really need to account for magnitude and phase, for example) and rarely worth the effort IME/IMO. Sensitivity is typically specified at one frequency with units of dB/W/m, so does not directly specify impedance, thus no easy way for the consumer (or professional) to do anything with it -- not enough information from just the sensitivity spec. I look at impedance plots mainly to determine the capability of the amp, but note that virtually any amplifier will double power into low (half-impedance) loads for brief transients, so it is not something I normally worry about.

Without knowing sensitivity over frequency, you could take the 1 kHz spec and ratio the number with resistance to estimate the demands at other frequencies. For example assuming 1 kHz dB/W/m is given, look at the impedance at 1 kHz, then ratio by the impedance at other points knowing power (W) = V^2/R so adjust the sensitivity for different R (impedance magnitude in ohms) values. If the number is 90 dB/W/m at 1 kHz and 8 ohms, then if the impedance dips to 4 ohms at 100 Hz, the effective sensitivity is reduced since now it takes 2 W instead of 1 W. The new number is 87 dB/W/m at 100 Hz and 4 ohms relative to the 1 kHz and 8-ohm spec (using the logarithm given before, 10*log10(1 W/2 W) = -3 dB so subtract 3 dB from the 90 dB/W/m rating). That assumes the frequency response is perfectly flat; if not, you'd have to factor that into the equation. It gets messy.

You could set up a program or spreadsheet to do the math if you have the frequency response and impedance magnitude numbers (or read from plots in reviews or from the manufacturer). At one time I did that, but it was many years ago, and I have not bothered since. This topic has come up before here and elsewhere but, like the cascaded gain and distortion/noise thread, it is hard to get enough information to make it useful in the real world so I've never tried to write it up.