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Approximating Headphone Volume Output (dB)

Discussion in 'Sound Science' started by tinyman392, Dec 21, 2011.
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  1. mikeaj
    Where is ear level measured?  Just with a mic in free space?  What's the difference in dB between ear level and in ear measurements, aside from gain above 1 kHz and so on due to the pinna and so on?  What's the difference in levels?
    My guess would be that something narrowband with X dB SPL total could be more damaging than something broadband with X dB SPL total, and so on.  Is that right?
    All I know is that A weighting is kind of abused in a lot of contexts.  It probably doesn't mean too much useful at higher levels, for music-like sounds.
  2. xnor
    As I wrote before, the formulas in the OP are wrong. In fact, complete nonsense.
    My attempts  to convince tinyman of using the proper formulas have failed. He's now using some kind of interpolation over at ifans. The last time I checked it still produced wrong results.
    With close to 20,000 views this is pretty irresponsible.
    On the comment above: proper dB SPL calculations are based on full-scale sine waves. Real music always has a lower RMS amplitude than full-scale sine waves even if completely unweighted so the results are conservative.
  3. RevMen
    I don't know.  And I don't think the OP knows, either, which is the point I was making.
    SPL, sound pressure level, is the ratio of sound pressure to the reference pressure squared, then converted to decibels.  Meaning SPL and dB are, in this context, the same thing.
    Well, see there's the problem I was pointing out again.  How are you combining your broadband sound into a single SPL?  There isn't such a thing as a broadband SPL unless you define a weighting scheme.  
    But I understand the gist of what you're saying and the answer is no.  It's the other way around.  If you're comparing a 1-kHz pure tone, which has a weighting of +-0 dB in the A-weighting scheme to a somewhat broadband sound with strong low-frequency content that is discounted by A-weighting, then the broadband sound has more actual energy and can therefore do more damage to your ears.
    Can you explain this?  I don't understand how there could be a difference between how sound pressure is measured and how it's calculated.
  4. xnor
    I don't see a difference either. Didn't say otherwise.
  5. mikeaj
    I thought it was just a typical energy or power calculation.  You first multiply by whatever weighting filter and then integrate over the frequency band.
    So I meant with same "area under the curve" (loosely speaking, and ignoring the weighting), it's worse to have something narrower and taller (looking at frequency on x axis, magnitude on y axis) than broader and shorter?  Or not.
  6. RevMen
    I guess I didn't ask my questions right.  Why would a different definition for SPL be used doing calculations vs measurement?  I wasn't aware of any definition other than 10log(Prms^2 / Pref^2)
    On the subject of how far off A-weighted levels can be from the levels predicted by headphone sensitivity, I pulled out my handy Larson Davis 831 and took a measurement in my living while I played some Tommy Noble.  Bandwidth matters very, very much...
    A-weighted, full spectrum:  78.6 dBA Leq
    1/1-octave, 1 kHz cf:  73.0 dB Leq
    1/3-octave, 1 kHz cf:  69.7 dB Leq
    FFT, ~83 Hz bandwidth, 1 kHz lf:  58.1 dB avg
    FFT, ~16 Hz bandwidth, 1 kHz lf:  42.4 dB avg
    All of those figures come from the same measurement.  Basically ALL of those values could be compared in some way to the SPL being calculated by the OP's method.  Notice that A-weighted is higher than all of them, by at least 5.6 dB, which is definitely enough to make a difference when it comes to hearing conservation.
  7. RevMen
    But remember that dB are logarithmic.  You can't integrate over the spectrum and get a meaningful result unless you first convert everything into pressure...

    ... meaning that a single, high frequency can be the controlling frequency.  A shorter, broader shaped curve will have a lower actual cumulative sound pressure than a narrower and taller curve with the same area (as long as we're in dB land).  And the way A-weighting works, you put a bunch of emphasis on a fairly narrow frequency region, so in effect you already are looking at a tall narrow version of the sound of interest.  Low frequencies won't have much impact on an A-weighted value, it's all in the 500-Hz to 4-kHz range.  So you can "sneak in" a bunch of low frequency energy with barely a motion on the A-weighted needle.
  8. mikeaj
    Oh, I haven't even read the OP.  (maybe I should have; sorry for confusion... let me fix that)  Thus I don't know about any mistakes that are there or maybe what you're responding to.

    Yes of course, that was implied ("multiply" doesn't make sense unless it's converted out of dB) but I should have been specific.  Obviously you need to do the calculations properly.

  9. RevMen
    I was responding to xnor in my first post.  Sorry, you snuck yours in while I was writing mine.
  10. ubikutz
    Hmm, let me ask you this than: I'm using the Fiio over USB, which i think means that there's no "input voltage" to speak of except standard USB and it's all happening internally the DAC.
    What i'm wondering is this: I have a multimeter and I can measure output voltage directly at the headphone jack given a certain volume setting, just to make sure i eliminate all other factors.
    Given that output current, the sensitivity and impedance of the headphones, is there a way to generate a resulting db value?
    Do i need to measure output impedance also?
  11. xnor
    First make sure your multimeter can measure AC and the supported frequency range. Then generate a the sine wave on your computer (any MM that can measure AC should be happy with 50 or 60 Hz, but my ancient Fluke measures even up to 500 Hz, so check the manual/specs if you want to use a higher frequency).
    While you are at it you can also measure the output impedance, but since it's very low in the E17 it shouldn't make much of a difference.
    To do that, play the generated sine wave, measure output voltage unloaded (= Vmax) and repeat the measurement (= Vl) with, e.g., a 30 Ohm (= R) or lower resistor in parallel.
    Zout = (Rl * (Vmax - Vl)) / Vl, for example: (30 * (2.6 - 2.2)) / 2.2 = 5.5 Ohm.
    To measure what the volume control is doing just measure a couple of volume control "positions" and plot those data points.
    Once you know the approximate output voltage at each volume control position we can go on.
  12. Jensigner
    here is a script calculator I wrote to help calculate dbSPL given either efficiency or sensitivity. It also includes a simple circuit to include any added series and/or shunt resistance (useful for some applications):
    I originally wrote this to help with using a line-out connection (not a headphone out) with specified output impedance to calculate how much dBSPL you would get with high-efficiency buds.
  13. mansurmojom
    Sir, the formula for current calculation is wrong I believe. It should not be like this
    Current = Voltage / Impedance
              =Voltage / ((1/R) + (1/R))
              =Voltage / (2/R)
              =(Voltage x R)/2
    Hence it comes out to be with impefance given
    Current = (Voltage x impedance)/2
  14. Jensigner
    My understanding is that the dBSPL ratings of headphones/iems are ALWAYS given as either dBSPL / 1Vrms (at 1 kHz)  or dBSPL / 1mW (at 1kHz) irrespective of how ear damage threshold values are specified (i.e. if they are A-weighed or not). Is this true?
    Also, I was interested in comparing the difference in dBL (no weighing) and dBA values for an ideal case of a FLAT noise spectrum. (I'm not sure if this is relevant to the headphone SPL discussion above however).  I calculate, (normalizing to 1 kHz) that the dBA value in this idealized case is almost exactly 2dB LOWER than the dBL value (which relates to how S/N is specified in audio gear?).   
    Update: I did some listening tests with my HD598 phones (nominal 50ohm  112 dBSPL/1Vrms @ 1 kHz or 99 dBSPL/1mW) and measured the rms voltage across the phones for 2 different cases while listening:
    - 1kHz pure sine wave
    - loud rock music with reasonably broad frequency spectrum
    For the 2 cases, I increased the volume until it was, according to my ears, just about too loud to bear for more than 20 sec. For the rock music case, the rms voltage was ~ 150mVrms while for the 1kHz pure tone, it was ~ 100 mVrms or 92 dBSPL (or about 3.5dB lower).
  15. xnor
    Yes, the sensitivity is usually measured at 1 kHz with a single tone, but sometimes a 500 Hz tone is used which should be explicitly specified.
    Depending on the frequency response of the headphone this can mean that a headphone with a peak at ~3 kHz, where our hearing is the most sensitive, will be more hearing damaging than another headphone with exactly the same sensitivity but without that ~3 kHz peak.
    It is a bit like the nominal impedance (e.g. 32 ohm). Real impedance in the audio range could range from 30 to 70 ohms.
    Regarding the other questions, maybe you can take something useful from http://www.head-fi.org/t/668238/headphones-sensitivity-impedance-required-v-i-p-amplifier-gain
    What is "dBL"? Measuring RMS voltage with a multimeter is not very accurate. Some only work properly with 50/60 Hz signals. My old Fluke is specified to measure more or less accurately up to about 500 Hz. I have no idea how it would deal with anything but single tones.
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