# Approximating Headphone Volume Output (dB)



## tinyman392

I originally posted this on another forum (iFans) here: http://www.ifans.com/forums/showthread.php?t=364522
   
  I do think that it is an important concept to get down for a headphone forum, so I am going to repost here as well.  Some disclaimers before I begin, I have double checked the units and they do add up to dB when multiplied out (stage by stage), so that part is accurate.  However, I still have to warn that these results may not be 100% accurate and will only give you a ballpark estimate at your actual listening levels.  The best way to get the actual number would to get a dummy head and an SPL meter (kind of expensive).  This method requires a calculator, and a little understanding of high school physics.
   
  On the other forum I did include a quick and dirty command line program (Windows only, sorry Mac and Linux users) that would calculate it for you granted you inputted correct information.  I don't know what the rules are like here concerning executables, so I won't upload it here.  It is uploaded on the other forum if you need it (it comes with source code to be compiled for other machines; use a C-based compiler).
   
  Again, no guarantees of 100% accuracy, but it will get decent numbers to give you a good estimate.  Let me know if you have any questions.  This guide also assumes that your volume bar increases voltage at a parabolic rate (what I found most devices to do: phones, iPods, laptops, etc).
   
  Quote: Tinyman392


> I don't know how many of you actually pay attention to this. However, a large volume output can really damage your hearing, even further, anything over ~75-85 dB can cause your ears to tune out low and high frequencies. This in turn can actually _decrease _the quality of your music (Inner Fidelity). Anything over 90 dB can damage your hearing if exposed too long.
> 
> Ideal listening levels should be around 60-80 dB. I generally listen myself around 70 dB (calculated). So how exactly do we calculate this (estimated) listening level? Well it's simple, first we need some information though:
> 
> ...


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## itchyblood

what's the max voltage output of a fiio e9?  I just find mW and ohms for that value.


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## Head Injury

Quote: 





itchyblood said:


> what's the max voltage output of a fiio e9?  I just find mW and ohms for that value.


 

 You can determine it from the ohms and mW. V = sqrt(R*W), R being ohms and W being mW/1000.
   
  I'll save you the trouble and say it's about 7 Vrms max, less into low impedances.
   
  Ah, on the subject, that's something the OP is missing. Output impedance can reduce the voltage into low impedances. Some amps are also current limited, so will get reduced power into low impedances.


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## tinyman392

Based on the 2V RMS conversion to peek voltage output, V RMS = V Peak / sqrt(2); the peak voltage is 2.8284 volts.  Please do note that this amp may not do do power output in a squared fashion like I have above.  It may actually do linear, but I"m not sure.  If it does do linear, don't square your (% of volume) when you do the actual voltage calculation...  I do know there are some amps that do this, I think FIIO might be one of those amps (don't take my word for it though). 
   
  Another way to get actual voltage output is to get an aux cable and connect it to a volt meter (one end goes to grounding contact while the other will go to one of the other contacts for either left or right).


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## tinyman392

Quote: 





head injury said:


> You can determine it from the ohms and mW. V = sqrt(R*W), R being ohms and W being mW/1000.
> 
> I'll save you the trouble and say it's about 7 Vrms max, less into low impedances.
> 
> Ah, on the subject, that's something the OP is missing. Output impedance can reduce the voltage into low impedances. Some amps are also current limited, so will get reduced power into low impedances.


 


  The post was mainly intended for portable devices as it came from an iPod forum, so I didn't modify it for anything.  That MaxVoltage*(%volume)^2 is actually a really special function that is unique to most laptops and mobile devices, as this is normally how they are hooked up to deliver voltage outputs.  That multiplier may have to be changed for different amps and dacs.  As you increase the volume on different devices, the actual increase in voltage may not follow that same parabolic increase I saw on my iPod.  Instead, it could be linear, or some other function of the volume output. If you know the actual voltage output (EG you measured it), you can change that whole equation there to just the actual voltage.  Otherwise, there will be some sort of relationship to the %volume and actual voltage output (with respect to the max voltage output): linear, squared, cubed, etc.
   
  But you are correct, this wasn't made with amps and other things in mind, for that I apologize.


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## Head Injury

Quote: 





tinyman392 said:


> Based on the 2V RMS conversion to peek voltage output, V RMS = V Peak / sqrt(2); the peak voltage is 2.8284 volts.  Please do note that this amp may not do do power output in a squared fashion like I have above.  It may actually do linear, but I"m not sure.  If it does do linear, don't square your (% of volume) when you do the actual voltage calculation...  I do know there are some amps that do this, I think FIIO might be one of those amps (don't take my word for it though).
> 
> Another way to get actual voltage output is to get an aux cable and connect it to a volt meter (one end goes to grounding contact while the other will go to one of the other contacts for either left or right).


 

 Where are you getting 2 Vrms for the E9? That's the line out, not headphone out. Use the power output at 600 ohms.
   
  V = sqrt(600 x 0.08) = sqrt(48) = 6.9 Vrms
   
  And at 16 ohms:
   
  V = sqrt(16 x 1) = 4 Vrms
   
  You can't ignore max current and output impedance even if you ignore amps. Portable players will be current limited into low impedance loads, and some will have impedances greater than 1 ohm. Using max voltage makes for a good estimate, but the only way to know for sure is to measure it.


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## itchyblood

Okay Thanks guys!


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## jcx

the Headwize site is archived, try the library:
   
http://gilmore2.chem.northwestern.edu/library.htm
   
   
  specifically for hearing safety:
   
http://gilmore2.chem.northwestern.edu/articles/hearing_art.htm


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## khaos974

I usually a different formula where the listening level is set by listening to regular music.
   
  dB(SPL) = S + 20 log ( Va / Vref )
   
  where:
   
  - dB(SPL) is the average listening volume for a track.
  - S is the sensitivity of the headphones expressed in dB/Vref, Vref is often 1V and the specification is dB/V
  - Vref is the reference voltage used in the dB/V spec, or the calculated one from the dB/mW spec ( Vref = sqrt (0.001 W * Zload)), Zload is the impedance of the headphones
  - Va is the 'average' voltage at the headphone output corresponding to to the listening volume and the specified track.
   
  Va = Vmax * 10 ^ ( (Gvc + Gtrack) / 20 ))            (1)
   
  where:
   
  - Vmax is the max Vrms output of the headphone out, usually 1 or 2 Vrms for on board computer outs
  - Gvc is the gain in dB set with the Windows volume control (2)
  - Gtrack is the level of your track compared to a 0 dBFS sine wave (3)
   
   
  (1)The idea comes from 20 log ( Va / Vmax ) = Gvc + Gtrack, that is to say that you need to subtract the gain of the volume control and the gain of the track to find the voltage output compared to the max voltage
   
  (2) Control Panel > Sound > Properties > Level > right-slick on the number and select dB. Gvc is - 15 dB in this case.
   

   
  (3) Gtrack is - 14 dB  in this case, the Dynamic Range Meter plugin for foobar is available here: http://www.jokhan.demon.nl/DynamicRange/index.htm
   

   
  NB: The above calculation takes into account the average level of the track, not the peaks, I find it a more accurate approximation of the average listening volume, It also assumes a 0 ohm output impedance, otherwise replace Vmax by Vmax * ( Zload / (Zload +Zout) ), where Zout is the output impedance and Zload the impedance of the headphones.


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## geetar7

Check-out this online calculator:
   
  http://www.headphone-amplifier.com/calculator.htm
   
  It took me a while to find this through google searches.  I have not verified their math or assumptions.  For example, comparing headphones must use the same units for effectivity or be referenced to the same impedance - tricky.
   
  A search for this link here on head-fi yielded several results.
   
  David


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## Atzki

Thank you very much for your post. It was REALLY what we need for our thesis project. My group is developing an android application that would estimate the headphone volume output among other things.

 My only problem is that I can't search for the device's (samsung mobile) maximum voltage output. The results just pertain to its battery (is that it? i kinda doubt it). So I really can't follow through..
	

	
	
		
		

		
		
	


	



 any suggestion, please?


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## Atzki

Ok. I've already satisfied my concern above. So anyway, as I've stated, I'm doing my thesis project and I would really like to use this as a reference of my formula but I think I need to prove that this is really credible--I AM convinced it is, only, I don't know how to explain that and defend this against the panelists. i would REALLY appreciate suggestions given asap. PLEASE.


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## arisu

The formulas given by tinyman392 and by khaos974 seem to give different results.

 From what I can understand, the difference comes from the following:

 tinyman392 assumes
  Quote: 





> SPL (Pa) = sensitivity(Pa/W) * power


 

 while

 khaos974 assumes
  Quote: 





> SPL (Pa) = sensitivity(Pa/V) * voltage


 

 where power = voltage^2 / impedience.

 Which one is correct ?  Or does it depend on choice of earphone ?


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## xnor

Sensitivity can be specified in both dB SPL/V or dB SPL/mW. It doesn't matter which you use as long as you don't mix up the formulas.
   
  Tinyman's formulas seem to be wrong.. also see this.


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## arisu

Quote: 





xnor said:


> Tinyman's formulas seem to be wrong.. also see this.


 
   
  Thanks for the link.
   
  Look like tinyman392's formula for actual output voltage might also be wrong then.
  Quote: 





> Actual Voltage (volts) = Max Output Voltage (volts) * (volume level fraction)^2


 
   
  Is ipod's volume level fraction linear to actual output level in dB as described in this ?  If yes, then we would expect actual voltage to be exponential to volume level fraction instead.


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## xnor

I don't have an ipod at hand so I cannot measure the volume control, but over -50 dB at 10% makes more sense than just -20 (or -40 for squared) dB. If the volume control was linear it would be pretty useless for sensitive IEMs.
   
  btw: -50 dB re 1 V = 10^(-50/20) = 0.00316 V .. should be a (very) comfortable level with sensitive IEMs


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## xnor

From what I've read on ifans tinyman seems to be pretty stubborn and prefers spreading nonsense than admitting that he's wrong. Somehow reminds me of Mr. amb.


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## d_headshot

Quote: 





khaos974 said:


> I usually a different formula where the listening level is set by listening to regular music.
> 
> dB(SPL) = S + 20 log ( Va / Vref )
> 
> ...


 
   
  The ATH-M50 doesn't specify sensitivity very well: http://kenrockwell.com/audio/audio-technica/ath-m50.htm
   
  I listened to a rock track that was about DR8, and -8.3dBFS RMS, and found that -35dB on windows volume to be decent, and then I tried -30dB which was quite a bit louder but not too loud. I'm not sure what the model of my soundcard is so I don't know what the Vmax is either. If that and the sensitivity could be clarified then I would like to know how loud in dBSPL I was actually listening to. That way I can gauge what's a safe volume to listen to for x hours. 
   
  Edit: I do also have the Denon AH-C560's and they are 16 ohms, and have a sensitivity of 110dB/mW. With the same track, I found my avg listening volume to be -43dB (which makes sense because they are more sensitive), and "comfortably loud" to be -38.9dB. To make sure I get these particular calculations right I'll just play around with an excel sheet and plop the formulas there. If anyone else has ATH-M50's on this thread, let's pick a sound file to use and compare how sensitive our own hearing is


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## mikeaj

If it's not specified, it's usually dB SPL / 1 mW input.  That also makes sense given peoples' impressions of the device.  It also matches Tyll's measurement at InnerFidelity of 0.13 mW needed for 90 dB SPL (so 98.9 dB SPL / 1 mW).
   
  You can measure the computer's max output with a cheap multimeter.  Just run a full-scale 60 Hz sine wave, and a cheap meter should pick that up with no problem.  Measure via say a 3.5mm male/male cable and probe the tip to sleeve (or ring to sleeve), or whatever is convenient.  Actually, it would be better to use a splitter and load the headphones while testing (reduce the level if necessary), in case the output impedance is not low, which is very possible.


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## d_headshot

How do you convert dB/mW to dB/Vref in the quoted post?
   
  I'm kind of confused because I know dBm is 10log(P/1mW) but when you have dB/mW(as in "per" 1mW), it's a ratio of dB to power, not a logarithmic reference


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## xnor

"dB/mW" means dB *SPL *with 1 mW of power into the headphones. Sensitivity is always about sound pressure. It has nothing to do with dBm, dBV etc.
   
  P = V * V / R
  V = sqrt(P * R)
   
  for a 30 ohm headphone:
  sqrt(0.001 * 30) = 0.1732 V
   
  Since the other sensitivity specification is referenced to 1 Vrms: 20*log10(1/V)
  for the headphone above:
  20*log10(1/0.1732) = 15 dB
   
  add that 15 dB to the sensitivity specified as "dB/mW".
   
   
  The other way:
  P = 1 * 1 / 30 = 0.0333 W
  10*log10(0.001 / 0.0333) = -15 dB


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## d_headshot

Ah so if a specification is rated in dBSPL/1mW, you must use a Vref in your calculation (in this case 0.1732) that was produced from the original impedance and 1mW parameters, rather than referencing 1V (because that was never used in the manufacturer spec). Our new conversion states that "we would get whatever amount of sensitivity when using 1V of signal, referenced to a voltage that would yield 1mW through whatever impedance we were testing. What I still don't get is that khaos is using an arbitrary 1V for his Vref rather than your voltage that actually comes from parameters that we have.
   
  Aside from making sense of the calculations, I did play around with excel and got some SPL levels within my avg volume and "comfortably loud" that are well below damage but they're using dBA rather than dBSPL so I'm not sure if my findings are meaningful. I did measure about 0.5Vpk of max output from my headphone out jack before clipping occurred and that seems pretty low considering the RMS will be even lower
   
  http://www.noisehelp.com/noise-dose.html
  http://www.noisehelp.com/decibel-scale.html


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## xnor

Yeah we're just calculating the difference in sensitivity for different input voltages. In the special case that the headphone's impedance is exactly 1000 ohms both sensitivity ratings would be equal.


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## sgrossklass

Bumpity-bump. You guys may be interested in the level calculation spreadsheet that I put together a while back. Ye olde sensitivity calculator (dB/mW <-> dB/V <-> dB/V@given R_out) is here.


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## LizardKing1

Quote: 





sgrossklass said:


> Bumpity-bump. You guys may be interested in the level calculation spreadsheet that I put together a while back. Ye olde sensitivity calculator (dB/mW <-> dB/V <-> dB/V@given R_out) is here.


 
   
  Thanks, that's a great tool. Found out I listen to almost-no-DR music in a very quiet environment at 52dB SPL (assuming output voltage or a rockboxed ClipZip is 800mV), which I think is good.


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## ubikutz

Hi guys,
   
  I've recently had trouble with my hearing in the form of tinnitus and hyperacusis (not caused by music but by environment noise), so I'm trying to make sure that during my private listening time, i'm staying well within the 60-70db limit to prevent further damage.
   
  Thing is i'm not so good with performing the calculus above, so I wanted to ask you if there's a way to approximate what would the 60db level be with my gear?
   
  I'm using a Sennheiser IE80 / HD598 with a Fiio E17 dac/amp with their specifications below.
  I'd appreciate some help, as from thereon I could manage to keep my listening well under control.
   
  Senn IE80 - impedance 16 Ω, sensitivity 125db 
  Senn HD598 - impedance 50 Ω, sensitivity 112db
  Fiio E17 - set on 0 gain, digital volume ranges from 0 to 60, full specs attached


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## xnor

It would also be helpful to know the max output voltage of your source.
   
  A Sansa Clip+ outputs about 0.5V max. The IE80 is highly sensitive so only needs very low voltage (1 to 2 mV) to reach that volume. With the amp set to have zero overall gain you'd have to set the volume on the Clip+ to about -50 dB.


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## ubikutz

Trouble is i'm not so good at electronics 
  Looking at the Fiio E17 specs from their website http://fiio.com.cn/products/index.aspx?ID=100000014895351
  I'd assume that the max output is:
   
   

 *Output Power* > 220 mW@32Ω /> 290 mW@16Ω 

   

 *MAX output voltage* > 7.3 Vp-p
   

 *MAX output current* > 80 mA


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## xnor

I was assuming you're using the aux input since the gain option doesn't seem to apply to the internal DAC, though I could be wrong on this one.
   
   
  7.3 Vpp / 2 = 3.65 Vp / sqrt(2) = 2.58 Vrms
   
  And when using the max power P = V^2/R so V = sqrt(P*R) = sqrt(0.29*16) = 2.15 Vrms
   
  To get the attenuation:
  for 2 mV: 20*log10(0.002 / 2.15) = -60.6 dB
  for 1 mV: 20*log10(0.001 / 2.15) = -66.6 dB
   
  How that relates to the digital 60-step volume control I really don't know. If you have a multimeter you should be able to measure the attenuation, or try to find somebody else who did that.


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## RevMen

I appreciate the math and the effort but I think this is potentially very irresponsible.  There's a serious mistake being made that, it seems to me, might mislead people into listening at unsafe levels, believing that they are safe.
   
  Quote: 





d_headshot said:


> but they're using dBA rather than dBSPL so I'm not sure if my findings are meaningful.


 
   
  A-weighting (dBA) and Sound Pressure Level (SPL) aren't two options from the same list.
   
  A-weighting is entirely in the frequency domain.  It takes a full-spectrum sound and applies weights to different frequency bands (roughly according to a human equal-loudness curve at 40-phons) and then adds all the bands up into a single number.
   
  You can have A-weighted SPL (with any time constant, whether slow or fast or whatever), sound power, continuous equivalent level (Leq), Ln, or however you want to measure in the time domain.
   
  And there's the problem I see with the original post.  It's mixing different SPL concepts.  The SPL that's measured to determine headphone sensitivity is a pure tone at 1000 Hz, measured in the (fake) ear canal.  I don't know what time constant is used.
   
  The SPL values that are said to cause hearing damage at such a level and comfortable listening levels and such are A-weighted, full-spectrum SPL ("slow"), and at ear level (not in-ear). This is not directly comparable to the SPL in the sensitivity measurement.
   
  It's possible for different types of music to result in very different A-weighted SPLs, even if they're adjusted so that their 1-kHz levels are the same.
   
  A-weighting can be a useful tool, but it grossly oversimplifies.  It's also usually quite incompatible with music.  Broadband noise, like machines running or highway traffic can be fairly well characterized with A-weighted figures.  But music often has exaggerated low frequency sounds that are effectively ignored by the A-weighting scheme, but still quite able to cause hearing loss.
   
  So please be VERY CAREFUL about telling people certain SPLs are safe when in reality it's very possible that THEY ARE NOT.  Please make sure you've got your decibels straight before you post anything that deals with people's health.  Make sure you understand the specifics of the dB you are using in both the frequency and the time domain, and make sure you don't equate different types of dB.


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## mikeaj

Quote: 





revmen said:


> The SPL values that are said to cause hearing damage at such a level and comfortable listening levels and such are A-weighted, full-spectrum SPL ("slow"), and at ear level (not in-ear). This is not directly comparable to the SPL in the sensitivity measurement.


 
   
  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.


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## 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.


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## RevMen

> Where is ear level measured?  Just with a mic in free space?


 
  Correct.
   


> 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?


 
  I don't know.  And I don't think the OP knows, either, which is the point I was making.
   


> What's the difference in levels?


 
  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.
   


> 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?


 
  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.
   


> 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.


 
  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.


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## xnor

I don't see a difference either. Didn't say otherwise.


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## mikeaj

Quote: 





revmen said:


> 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.


 
   
  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.


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## 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.


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## RevMen

Quote: 





> Originally Posted by *mikeaj* /img/forum/go_quote.gif
> 
> 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.


 
  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...

 Quote: 





> 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.


 
  ... 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.


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## 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.
   



revmen said:


> 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...


 
   
  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.


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## RevMen

I was responding to xnor in my first post.  Sorry, you snuck yours in while I was writing mine.


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## ubikutz

Quote: 





xnor said:


> I was assuming you're using the aux input since the gain option doesn't seem to apply to the internal DAC, though I could be wrong on this one.
> 
> 
> 7.3 Vpp / 2 = 3.65 Vp / sqrt(2) = 2.58 Vrms
> ...


 
   
  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?


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## 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.


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## 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):
      http://www.jensign.com/S4/calc.html
  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.


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## 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


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## 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).


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## 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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## Jensigner

Quote: 





xnor said:


> ---
> 
> 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.


 
   
  Thanks for the useful comments and reference. I'll check it out.
  dBL as in:
  "Unweighted sound pressure level is called "linear sound pressure level" and is often written as dBL or just L"  (wiki info).
  I didn't measure the rms voltage with a voltmeter. I wrote an application which uses a high-end sound card and samples at 24bit/96kHz and computes the real rms voltage and calibrated with a precision voltage source. It seems to be accurate (~ 10%) up to 20kHz.


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## xnor

Oh okay, so the Vrms figure is more or less accurate, but that doesn't necessarily translate well to perceived loudness or measured weighted SPL. There's also still the problem with headphone frequency response.


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## Jensigner

Quote: 





xnor said:


> Oh okay, so the Vrms figure is more or less accurate, but that doesn't necessarily translate well to perceived loudness or measured weighted SPL. There's also still the problem with headphone frequency response.


 
  Yes I agree with that. I think the only useful comparison (and it is only at one frequenc so is really of limited practical use and give a very rough idea of overall "loudness") is the spec'd dbSPL at 1 kHz for either 1 mW or 1Vrms. Being a Physicist, I like to "assume it's a sphere"


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## AbsoluteZero

Interested in these things but still confused.
   
  First, I am feeding my music through an Apex Glacier which says the following in Maximum Output : 3.3V RMS into 15 Ohms; 2.14V RMS into 33 Ohms. Anyone care to decipher what that means and also which numbers can I extract as information?
   
  The Apex Glacier manual also stated that each step on the wheel is exactly 2 dB so is it correct if I assume this to be linear instead of logarithmic in the calculation? (there are 32 steps, I listen at around 10 to 16 steps)
   
  Also I have a headphone with 102 dB SPL/mW, 60 ohms impedance if anyone would kindly help me find my loudness number 
	

	
	
		
		

		
			





.
   
  Thanks guys!


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## xnor

Specs on ttvj website say:
  [size=10.0pt]Maximum output: >2.6V RMS into 150Ω; >1.7V RMS into 32Ω[/size]
[size=10.0pt]Maximum gain:  0dB, 10dB, or 20dB, ±<0.5dB[/size]
[size=10.0pt]Maximum input level: 2V RMS[/size]
   
  So with a 2V source you don't need any gain (0 dB) in order to reach (close to) max output into 60 ohms.
   
  102 dB SPL/mW = 114 dB SPL/V
   
  so at full volume: 120 dB SPL (+6 dB because of 2V source)
  at step 29: 114 dB SPL (120 - 3*2)
  at step 16: 88 dB SPL (120 - 16*2)
  at step 10: 76 dB SPL (120 - 22*2)
   
   
  This is with a full-scale 1 kHz tone. *Real music will have a lower average SPL*, but can have short term peaks reaching close to those numbers.


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## Jensigner

Quote: 





absolutezero said:


> Interested in these things but still confused.
> 
> First, I am feeding my music through an Apex Glacier which says the following in Maximum Output : 3.3V RMS into 15 Ohms; 2.14V RMS into 33 Ohms. Anyone care to decipher what that means and also which numbers can I extract as information?
> 
> ...


 
  Assuming roughly that at 60 ohm load, we have ~ max output voltage of 3.3Vrms, then here are some results:
   
  A 2 dB step per volume increment means the output voltage factor is reduced by a FACTOR of 0.794  (or the POWER is reduced by a factor of 0.631).  So, these are the output voltages (pure sine wave) and assuming Z(1 kHz) = 60ohm with 102 dBSPL/mw or 114 dBSPL/1Vrms @ 1 kHz:
   
    10 setting:  21 mVrms      (22 dB below max setting)  giving  80 dBSPL at 1 kHz
    16 setting:  82 mVrms      (16 dB below max setting)   giving 92 dBSPL at 1 kHz
   
  Result using this calculator:   http://www.jensign.com/S4/calc.html


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## AbsoluteZero

Quote: 





xnor said:


> Specs on ttvj website say:
> [size=10pt]Maximum output: >2.6V RMS into 150Ω; >1.7V RMS into 32Ω[/size]
> [size=10pt]Maximum gain:  0dB, 10dB, or 20dB, ±<0.5dB[/size]
> [size=10pt]Maximum input level: 2V RMS[/size]
> ...


 
   
   
  Quote: 





jensigner said:


> Assuming roughly that at 60 ohm load, we have ~ max output voltage of 3.3Vrms, then here are some results:
> 
> A 2 dB step per volume increment means the output voltage factor is reduced by a FACTOR of 0.794  (or the POWER is reduced by a factor of 0.631).  So, these are the output voltages (pure sine wave) and assuming Z(1 kHz) = 60ohm with 102 dBSPL/mw or 114 dBSPL/1Vrms @ 1 kHz:
> 
> ...


 
   
  Thanks guys for the calculations, I am starting to understand these things currently.
  Now I can calculate for my other headphonesin my inventory, cheers!


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## Jensigner

Quote: 





absolutezero said:


> Thanks guys for the calculations, I am starting to understand these things currently.
> Now I can calculate for my other headphonesin my inventory, cheers!


 
  Glad to help out in some way. Related to audio level, I recently have built some basic gear to verify audio specs (typically "A-Weighted in a 20 kHz BW" noise and S/N) of some audio equipment I have. This is a very interesting area and opinions are strong (as you can see from the references I include):  http://www.jensign.com/AWeight/


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## luisdent

tinyman392 said:


> I originally posted this on another forum (iFans) here: http://www.ifans.com/forums/showthread.php?t=364522
> 
> I do think that it is an important concept to get down for a headphone forum, so I am going to repost here as well.  Some disclaimers before I begin, I have double checked the units and they do add up to dB when multiplied out (stage by stage), so that part is accurate.  However, I still have to warn that these results may not be 100% accurate and will only give you a ballpark estimate at your actual listening levels.  The best way to get the actual number would to get a dummy head and an SPL meter (kind of expensive).  This method requires a calculator, and a little understanding of high school physics.
> 
> ...


 
  
 I haven't read this whole thread, but I see a potential flaw in this calculation.  If you use all the variable and figure out your decibel level that you are supposedly listening to, how do you determine the level of the music as well?  In other words, the result of this calculation tells you the potential max db level you're listening to, but some songs are quieter than others.  If you change nothing with the volume, but switch to a quieter track this calculation won't reflect that (unless I missed something).  So if track two is 20db quieter than track one, how do you know how loud either track is?  Is this formula based on listening to a song that is a wall of 100% db of noise?  Just curious...


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## xnor

His old calculations were completely wrong. It's best to ignore them.


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## luisdent

xnor said:


> His old calculations were completely wrong. It's best to ignore them.



Is there any way to know your db without a measurement device?


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## xnor

Add to the sensitivity specified as x dB SPL/1 Vrms the following: 20*log10(V)
  
 That's peak. For a more realistic average see http://www.head-fi.org/t/668238/headphones-sensitivity-impedance-required-v-i-p-amplifier-gain (scroll down).


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## Farhan Zulkipli

tinyman392 said:


> I originally posted this on another forum (iFans) here: http://www.ifans.com/forums/showthread.php?t=364522
> 
> I do think that it is an important concept to get down for a headphone forum, so I am going to repost here as well.  Some disclaimers before I begin, I have double checked the units and they do add up to dB when multiplied out (stage by stage), so that part is accurate.  However, I still have to warn that these results may not be 100% accurate and will only give you a ballpark estimate at your actual listening levels.  The best way to get the actual number would to get a dummy head and an SPL meter (kind of expensive).  This method requires a calculator, and a little understanding of high school physics.
> 
> ...


Hello Tinyman. I'm 15 years old and not experienced in these things. Be nice to noobs hey  Anyway, I've been having this tinnitus for the past few days and have not managed to go to school yesterday and today. I use a First Gen FIIO X3 and I listen to it on around 60/120 volume although i go higher on my computer do to it being to softer. I was wondering, what is the max volume it can go to with a Brainwavs HM5. specs for both devices are here
Brainwavs HM5- https://www.amazon.com/Brainwavz-HM5-Studio-Monitor-Headphones/dp/B006MA9XXM
Fiio x3 First Gen - http://www.fiio.net/en/products/41/comparisons and http://ohm-image.net/opinion/audiophile/sound-quality-review-fiio-x3
Please oh please help me. I am so paranoid right now.


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