Weird trend when testing how power alters decibels, measured using a microphone 1 metre away. Why is this the case?

[u/Isosceles_Iso]

Additionally, its to note that this was after several repeated trials so random error has been ruled out.

[u/PerAsperaDaAstra]

Without knowing more about your experiment it's hard to say exactly, but most likely you're just seeing the response of your speaker be imperfect (nonlinear), possibly mixed with some calibration for your microphone.

[u/mmazing → u/PerAsperaDaAstra]

Also the dynamics of the room, etc.

[u/kleinerDienstag → u/mmazing]

The dynamics of the room are very unlikely to be nonlinear. Assuming OP kept the frequency content of the test signal constant, the emitted and received sound pressure should be proportional over a wide range.

[u/mmazing → u/kleinerDienstag]

That makes sense, I think I was naively assuming that the room might affect the output based on whatever frequencies might interact with various geometry …. and that must be at play.

However it makes sense that if the frequency isn’t changing the room shouldn’t be a huge factor.

Total side question- can I interpret this graph as “3dB is double the loudness” as 5w was ~62dB and 10w was ~65dB? I have always heard anecdotally that a 3 decibel increase is double the volume. No idea if true or relevant to this graph tho, haha.

[u/PerAsperaDaAstra → u/mmazing]

wrt. your side question, yes roughly. Decibels are a logarithmic base-10 unit of power relative to some reference. To convert x decibels to power/intensity, use the formula:

P = 10 ^{x / 10dB} P0

where P0 is the reference power/intensity (for audio stuff is usually the threshold for human hearing around 0.98 pW/m²⁾ Notice if x = 3dB then P is 10^3/10 = 1.9952623149688795 ≈ 2 times the reference, so every 3dB is about a doubling of the intensity.

(note: when OP says power, they likely mean power supplied to their speaker not measured power at the microphone, but their plot should still show something like a log dependence if their speaker was ideal - it likely isn't and is increasingly inefficient at converting the input power to measured sound at high powers, breaking the law to the messy curve they are seeing. Also they're plotting a small enough window that the log looks near linear here).

[u/mmazing → u/PerAsperaDaAstra]

Awesome thank you for the great response! ❤️

[u/val_tuesday → u/mmazing]

Depends what you mean by volume. 3 dB is roughly double the power, 6 dB roughly double the amplitude. Human perception has roughly 10 dB as a subjective doubling of loudness(!).

[u/val_tuesday]

You could be making all kinds of systematic errors in measurement, impossible to say with almost zero detail of the setup given.

Looks like the start has 3 dB increase per doubling of power, which is what you’d expect for a linear system. Then the curve plateaus. No way for us to know if that is measurement error or non-linearity in the device under test.

Assuming this is a speaker, the non-linear bit may be the amplifier (depending how/where you are measuring the power), the speaker, or even the microphone (though this seems unlikely as they tend to just clip at max level). The room/reverb/standing waves etc. can be assumed to be perfectly linear so should not affect this measurement.

Edit: actually the middle of the graph looks like the log curve you’d expect as well. Definitely plot the data with a log x-axis to see a clearer picture.

[u/Arve → u/val_tuesday]

I suspect that this experiment has been done with a wiper-style potentiometer or fader. These are typically notoriously non-linear as signal attenuation approaches infinity. This can often be heard for stereo equipment where one channel will go silent noticeably before the other.

[u/val_tuesday → u/Arve]

That isn’t the sense of the term non-linear that is meant and that would result in something other than the expected log curve for this particular measurement series.

What is meant by “linear” is a linear system, that is one which will commute with a linear combination of signals. So you get the same result whether you apply the system first and afterwards scale and mix the results or you first scale and mix and then apply the system.

Such a linear system will always exhibit the property that a scaling of the input will result in the same scaling at the output (this is part of the definition of linearity).

[u/Arve → u/val_tuesday]

Let me rephrase: I’m doubting that the X axis on this graph is actual power.

OP should re-do the experiment, but:

1. Plot voltage instead of power.
2. Loudspeakers have many nonlinearities, and they should properly be controlled for.

An output of 58 dB for makes pretty much no sense - speakers/speaker drivers typically have a sensitivity of 78-92 dB for 2.83V, measured at 1m. (This translates as 1W/1m for 8Ω nominal impedance). That there is such a huge disparity between what the graph shows and what calibrated measurement gear shows makes thinking this experiment has obvious gotchas like I stated entirely reasonable.

[u/val_tuesday → u/Arve]

Ah yes. I get your point and I agree that the explanation for the weirdness is most likely some simple error.

To be fair to the OP though, it doesn’t actually state what the reference is for the dB scale. If it is in fact dB SPL (ie. RMS pressure wrt. 20 uP iirc) then yes this speaker is weirdly inefficient.

[u/Worldly-Device-8414]

Surface/room/object reverb might be involved if the measurement lasts longer than reflection paths?

[u/DaveBowm]

The graph shows the composite effects between the various nonlinearities involved in the measurements. Most of these nonlinearities have a physical origin. They would be: nonlinearities in the means of measuring the driving electrical power involved, in the speaker's transduction of electrical power into sound power, in the receiving microphone's transduction of sound power back into electrical power, in the calibration and operation of the sound level meter's circuitry for determining the dB sound level. There is also a nonlinearity in the mathematical definition of how the dB level relates to the actual intensity.

One can at least remove and separate out the effects of this last mathematical nonlinearity from all the physical ones by simply graphing the data as a semi-log graph where the horizontal power axis is logarithmic and the vertical dB axis is linear.

[u/nsfbr11]

What exactly is the power that is being plotted? What is the sound spectrum being played? What is the design of the speaker? What is the microphone?

All those are potential sources of systematic non-linearities.

Edit: as part of my physics undergrad I took a grad acoustics engineering class as a free elective so it has been a lot of years (1985 grad) but I’d be happy to help if you try and flesh out the above.

[u/ci139]

you must distinct in between

• power (& wave form) to spk
• power (& wave form) to (near field) spl
• (semi near/far field) spl power (& wave form) to mic dynamic (mech.) disturbance
• mic dynamics to (unloaded) induced (electrical) power
• mic induced (electrical) power to metering circuitry output

? where you measure your "Power (Watts)"

? what assures your "Decibels (dB)" is proportional to the spl at near your mic

--other--

you should not only repeat the experiment but change the vector and distance of your mic
--or/and--
swap in between multiple sources and receivers
--or--
pre-verify that what you think is happening . . . is that what actually happens

[u/Moistinterviewer]

Also standing waves