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# Approximating Headphone Volume Output (dB) - Page 2

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

Edited by xnor - 2/23/13 at 4:30am

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.

Quote:
Originally Posted by 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.

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

Edited by d_headshot - 3/15/13 at 6:03pm

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.

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

Edited by d_headshot - 3/15/13 at 6:45pm

"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)

sqrt(0.001 * 30) = 0.1732 V

Since the other sensitivity specification is referenced to 1 Vrms: 20*log10(1/V)

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

Edited by xnor - 3/15/13 at 7:13pm

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

Edited by d_headshot - 3/16/13 at 9:19am

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.

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.

Edited by sgrossklass - 3/25/13 at 9:42am
Quote:
Originally Posted by 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.

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.

Edited by LizardKing1 - 3/28/13 at 11:57am

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

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.

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

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.

Edited by xnor - 5/7/13 at 9:20am

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:

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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