Safe listening levels and headphone voltage/power requirements

[xnor]

Heya,

there's a couple of threads asking about safe listening levels and people asking about voltage/power requirements in almost any amp/headphone thread.
Here's my take on this:


Noise Exposure Limits
The EPA and WHO recommend that noise should be kept below 70 dBA over 24 hours and below 75 dBA over 8 hours. Additionally, the CDC makes the rough recommendation to keep noise exposure below 2 hours for 80-85 dBA loud noise as (based on the same data and 3 dB exchange rate) to prevent hearing damage.

NIOSH defines a 3 dB exchange rate: permissible exposure time halves for every 3 dB increase in noise intensity.
NIOSH recommends a limit of occupational noise exposure to 85 dBA over an 8-hour time-weighted average.
EPA recommends noise exposure to be limited to 85 dBA over 45 minutes.


Why this discrepancy? The answer is in the:


Fine print
The EPA limits were chosen to protect 96% of the general population against impairment of physical (hearing loss) and mental (like discomfort) health.
The NIOSH limits were chosen solely to protect against hearing loss in the workplace accepting that 8% of the workforce will still develop hearing loss.
Therefore, NIOSH recommends hearing protection if noise levels exceed 85 dBA regardless of exposure duration.

The EPA limit is averaged over 24 hours.
The NIOSH limit is averaged over 8 hours (average workday) with rest/recovery periods between exposures.

The EPA limit is based on 365 days/year exposure.
The NIOSH limit is based on 250 workdays/year exposure.

The NIOSH limit considers implementation cost for businesses to stay within limits (sacrificing human health for economic reasons).

Note: both recommendations are based on audiometric tests of hearing loss up to 4 kHz.
Note: OSHA (which records occupational hearing loss cases) defines a significant decrease in hearing as a "standard threshold shift" which is a change of 10 dB averaged over 2, 3, and 4 kHz.


A-Weighting
A-weighting significantly attenuates low frequencies, while giving a slight boost to frequencies between 1 kHz and 6 kHz (the peak is about +1.3 dB at 2.5 kHz):



Conclusions
85 dBA should not be considered a universally safe limit, especially not for children, people with sensitive hearing, when regularly listening for several hours, or when being exposed to other potentially louder noise sources throughout the day.
Therefore, I recommend to stay below 85 dBA when listening to music.



Power/Voltage Requirements
This depends on headphone sensitivity and type of music you're listening to:


Headphone sensitivity
You can find this in product datasheets. If it's just specified as "x dB" then it is usually at 1 mW. Sensitivity is sometimes also specified at 1 Vrms.
Both are typically measured with a 500 Hz or 1 kHz sine wave.

To convert from dB SPL@1 mW to dB SPL@1 Vrms and vice-versa, calculate:

sensitivity_Vrms = sensitivity_mW - 10*log10(0.001 * impedance)
sensitivity_mW = sensitivity_Vrms + 10*log10(0.001 * impedance)

Note that a sine wave's RMS value is 3 dB lower than its peak magnitude. This needs to be considered when we analyze the RMS value of music tracks.
Additionally, we have to apply the A-weighting.


Music
Let's look at two extremes: classical recordings and highly dynamic range compressed modern pop/rock.
Note: the selection of tracks used for this analysis is random. Ymmv.


Classical:

Total RMS value: -24.1 dB
Total RMS value with A-weighting: -26.85 dB.

Modern pop/rock


Total RMS value: -11.2 dB
Total RMS value with A-weighting: -15 dB.

The differences in A-weighting (-2.75 dB for classical and -3.8 dB for modern pop/rock) is explained due to the fact that modern pop/rock has significantly more energy in bass/lower mids and also upper treble, which is exactly what the A-weighting filter attenuates.


So how much power/voltage do I need?
Now we have all the information we need:

• The target SPL: 85 dB SPL
• Sensitivity in dB SPL either @1 mW or @1 Vrms
• Weighted total RMS value

Note: for a 1 kHz sine wave, the weighted total RMS value would be -3 dB, hence the need to subtract an extra 3 dB from the target SPL.

power_mW = 10^((target_spl - sensitivity_mW - weighted_rms - 3)/10) voltage_rms = 10^((target_spl - sensitivity_Vrms - weighted_rms - 3)/20)


Amplifier gain, volume setting and headroom
Knowing the required voltage and the output voltage of your source device, calculating the required gain with optional added headroom is as simple as:

headroom_x = 10^(headroom_dB/20)
min_amp_gain_x = voltage_rms/source_rms * headroom_x
min_amp_gain_dB = 20*log10(min_amp_gain_x)

The actual gain of your amp may be higher, which means you'll have to turn down the volume. By how much? Calculate:

volume_x = min_amp_gain_x / amp_gain_x
volume_dB = 20*log10(volume_x)

I've also published a Headphone power spreadsheet that contains these calculations. Feel free to clone/download it.




Sources

1. CDC. What Noises Cause Hearing Loss?. https://www.cdc.gov/nceh/hearing_loss/what_noises_cause_hearing_loss.html
2. EPA [1974]. Information on levels of environmental noise requisite to protect public health and welfare with adequate margin of safety. EPA/ONAC 550/9-74-004. http://nepis.epa.gov/Exe/ZyPDF.cgi/2000L3LN.PDF?Dockey=2000L3LN.PDF
3. NIOSH [1998]. Criteria for a recommended standard: occupational noise exposure. DHHS (NIOSH) Publication Number 98-126. https://www.cdc.gov/niosh/docs/98-126/

 

[Soundescape]

Thanks for the spreadsheet.

Can you explain a bit what kind of info it need to be extracted from the amp datasheet to fill the spreadsheet?
I am a little bit confused as many values are calculated but I don't find exactly the same. Often I found output levels specified at specific gain level in the datasheet.

E.g. I don't know if can make a pratical example with this datasheet to show how we could fill the spreadsheet:

DX5 DAC\u0026amp;Headphone Amp-TOPPING

The headphone data section is clear.

 

[Lambda]

you seam to ignore Time weighting? https://www.nti-audio.com/en/support/know-how/fast-slow-impulse-time-weighting-what-do-they-mean

Therefore, I recommend to stay below 85 dBA when listening to music.

The target SPL: 85 dB SPL

But the Target shuld be A waited RMS value (or other time weighting) not dB SPL peak.
Peak is relatively irrelevant, and as you showed yourself Total RMS value with A-waited value can easily be 25dB lower depending on music

 

[xnor]

Thanks for the spreadsheet.

Can you explain a bit what kind of info it need to be extracted from the amp datasheet to fill the spreadsheet?
I am a little bit confused as many values are calculated but I don't find exactly the same. Often I found output levels specified at specific gain level in the datasheet.

E.g. I don't know if can make a pratical example with this datasheet to show how we could fill the spreadsheet:

DX5 DAC\u0026amp;Headphone Amp-TOPPING

The headphone data section is clear.

Sure.

Since this is a combo DAC/amp, you can either (1) enter a fixed source voltage (some reference like 1 or 2 Vrms) and appropriate low/high gain values, or (2) you can set the gain to 0 and just set your product's max output voltages as source voltage.

Case 1)
Source Voltage [Vrms]: 1 (because Topping specifies the gain settings relative to 1 Vrms)
Amp gain [dB]: +6.7 or +19 directly from the spec sheet (depending on the gain setting on the device)

Case 2)
Source Voltage [Vrms]: 2.12 or 8.84
Amp gain [dB]: 0

If you're wondering where these voltages are coming from: Topping specifies 6 Vpp (low gain setting) and 25 Vpp (high gain setting) as max output voltages.
Conversion between Vpp (peak to peak), Vp (peak) and Vrms is quite easy:

Vp = Vpp / 2
Vrms = Vp / sqrt(2)

 

[xnor]

you seam to ignore Time weighting? https://www.nti-audio.com/en/support/know-how/fast-slow-impulse-time-weighting-what-do-they-mean

Yes, because this is not about displaying SPL in realtime but integrating over the entire duration.
According to the 3 dB exchange rate, a tone with a duration of 1 and an amplitude of sqrt(2)^n (that's n times +3 dB) has the same "hearing damaging" energy as the same tone with a duration of 2^n with an amplitude of 1.
This can be summarized in a single number: total RMS amplitude.
https://www.nti-audio.com/en/support/know-how/fast-slow-impulse-time-weighting-what-do-they-mean

But the Target shuld be A waited RMS value (or other time weighting) not dB SPL peak.
Peak is relatively irrelevant, and as you showed yourself Total RMS value with A-waited value can easily be 25dB lower depending on music

None of the values are peak values. They are all RMS, or in this case the average dB SPL, A-weighted.
To repeat my previous point, this average is over the entire duration.

Short-term, the dB SPL (weighted or not) can and will fluctuate quite wildly around that target value.
For example, when I analyze my "classical" music sample using a 50ms window, the top RMS amplitudes are over +18 dB higher the total.
For the "modern pop/rock" music sample these fluctuations in short-term dB SPL are naturally smaller, because the music has been compressed so much in its dynamic range. Over a 50ms window the loudest portions of the track are about +9 dB over the total.

As for your objection: yes, you're correct.
I had added the term "weighted" to the spreadsheet a couple of days ago, because in theory you could also do this with any other weighting filter and not just A-weighting, but I cannot do the same here since I'm not allowed to edit old posts.

 

[solderdude]

Therefore, I recommend to stay below 85 dBA when listening to music.

85dBA average can have peaks up to 100dB peaks which is 'comfortably loud'.
Most (normal) people only listen at this level for the duration of 1 or 2 songs and then get the urge to dial down a bit.

Noise is not the same as music though but some music is just noise to me.

I've also published a Headphone power spreadsheet that contains these calculations. Feel free to clone/download it.

I also published a similar kind of list.
Last updated it in 2020 and looks like it needs an update again... maybe next year.

 

[xnor]

One more thing regarding the spreadsheet:
You should check if your amp can actually achieve the required power/voltage into your load (headphones).

Using @Soundescape's example, even though the spec sheet says ~8.8 Vrms at high gain, that does not mean that amp can actually output that into every headphone:

For example, from amir's DX5 measurements:

you can see that the amp clips at roughly 3 Vrms if driving a 12 ohm load.

Let's say you had crazy inefficient 80 dB/mW 12 ohm headphones that according to the spreadsheet would need about 3 Vrms output for the "classical" music setting.
With the high gain value of the DX5 entered into the spreadsheet, nothing would turn red because 3 Vrms is smaller than the theoretical ~8.8 Vrms output.

In reality, you would be in limiting/clipping territory of the amp. Since the "classical" music setting assumes high dynamic range, only the highest peaks in the music would be distorted.

The spreadsheet would also say that your volume (with overhead set to 0 dB) is only at -9 dB, but turning up the volume beyond this point would just cause more and more of the music to become distorted. Depending on the product this could also trigger protection mechanisms.

 

[xnor]

85dBA average can have peaks up to 100dB peaks which is 'comfortably loud'.
Most (normal) people only listen at this level for the duration of 1 or 2 songs and then get the urge to dial down a bit.

That roughly lines up with my numbers. In #5 I described how a 50ms window gives me +18 dB RMS amplitudes vs the total for the "classical" sample. As the window size is reduced towards the sampling period, this number approaches the sample peaks, which is roughly +24 dB unweighted and +26 dB weighted. But these events will not be perceived as such and are also quite rare. (Btw, I'm aware that "rare" is meaningless and what I should be doing is posting the distributions, but I have something else I want to post first.)

Also @Lambda: These higher short-time amplitudes in the "classical" sample are paid for by a lower average RMS amplitude such that the total stays right on our 85 dBA target. (Remember, every +3 dB halves the allowed duration.)
For comparison: the "modern pop/rock" sample has much smaller ~8.5 dB peaks vs the total using the same 50ms window.

I also published a similar kind of list.
Last updated it in 2020 and looks like it needs an update again... maybe next year.

Thanks but your link appears to be broken.

 

[Soundescape]

Sure.

Since this is a combo DAC/amp, you can either (1) enter a fixed source voltage (some reference like 1 or 2 Vrms) and appropriate low/high gain values, or (2) you can set the gain to 0 and just set your product's max output voltages as source voltage.

Case 1)
Source Voltage [Vrms]: 1 (because Topping specifies the gain settings relative to 1 Vrms)
Amp gain [dB]: +6.7 or +19 directly from the spec sheet (depending on the gain setting on the device)

Case 2)
Source Voltage [Vrms]: 2.12 or 8.84
Amp gain [dB]: 0

If you're wondering where these voltages are coming from: Topping specifies 6 Vpp (low gain setting) and 25 Vpp (high gain setting) as max output voltages.
Conversion between Vpp (peak to peak), Vp (peak) and Vrms is quite easy:

Vp = Vpp / 2
Vrms = Vp / sqrt(2)

Thanks this is a confirmation of the values I've used.

Two points:
1) the difference between Classical and Rock it is quite huge. It will be not easy to adapt the volume for every track and still be in the "safe zone". Also what will be the role of LUFS normalization in many streaming services?

2) Many popular eq presets (autoeq, @oratory1990, etc..) will require to use a negative gain to avoid clipping. This will often negativaly impact the LUFS so I suppose that it will be hard to understand how to compensate the values in the spreadsheet.

 

[xnor]

So here's another thing I wanted to clarify: there's a common misconception about what frequency spectrum plots show.

People keep on saying that in music there's much more energy in the low frequencies than in the mids and highs. Even amirm did this in his "Music: how loud is loud?" video.
They always point at a log frequency plot, showing a drop of amplitude with increasing frequency.

The first hint that this is questionable is the fact that the spectrum of pink noise (which drops 10 dB/octave and is said to approximate the spectrum of music) is such that each octave interval has the same amount of energy.
So the statement is definitely wrong for pink noise. How wrong is it for music?

To clarify my point, let's take a look at white noise which has a flat spectrum.
If we filter the noise with two bandpass filters centered around 20 Hz and 2000 Hz and an octave-wide bandwidth (that's a factor of 2x, equal bandwidth in log space), we get this picture:

So how much energy is in each of those two bands? Using the amplitude comparison approach, the energy should be the same, right?
But that's wrong. The total RMS amplitude of the band on the left is 20 dB lower. Why? Because it has 1/1000th (-20 dB) the bandwidth of the band on the right.

Again: there's a 20 dB difference here that's not easy to see because we're looking at it on a log frequency scale. This visualization makes sense since our hearing is also logarithmic, but it also causes this misinterpretation.

Let me introduce a correction that I'll call "log-compensation":

The compensated curve accounts for the difference in energy on a logarithmic frequency scale. Now the energy contained in each log(Hz) can be compared just by looking at the amplitude!
The left band now has a 20 dB lower amplitude than the right band, which matches the difference in RMS amplitude between those two bands.


Looking at the spectrum of our music samples:

​

The classical sample roughly follows the 10 dB/octave drop from 100 Hz to 1 kHz.
But look at the log-compensated curve: it's rising in the same range! So there less energy in bass than in the mids per log(Hz)!
I also compared the RMS amplitudes of octave-wide bandpass filters centered around 100 Hz and 1 kHz: +2.4 dB.



The pop/rock sample shows hugely boosted bass, which results in a much steeper drop.
While the compensated spectrum is quite flat from ~400 Hz to 4000 Hz, there's still a visible boost in the bass region.
Comparing RMS amplitudes using the same filters as above: -3.6 dB.


This also explains why A-weighting does not result in hugely different numbers, which is another misconception that people have, even though it attenuates 20 Hz by 50 dB.

 

[solderdude]

Thanks but your link appears to be broken.

https://diyaudioheaven.files.wordpress.com/2013/03/headphone-power-table-2.pdf

this should work

 

[amirm]

 

[Peluvius]

Does anyone know if the information the Apple watch gives is relevant for listening to music? There is an audio app that tells you safe/loud and tells you how long you can listen for. Says the measurement is A weighted.

 

[xnor]

@amirm Yes, I also mention your video in #10 where I show that the claim that "there's much more energy in bass than mids/highs" is not necessarily true.

Short summary: there's 2.4 dB less and 3.6 dB more bass in my classical and modern pop/rock samples respectively when comparing 100 Hz to 1 kHz with an octave-wide bandpass filter.

 

[xnor]

Thanks this is a confirmation of the values I've used.

Two points:
1) the difference between Classical and Rock it is quite huge. It will be not easy to adapt the volume for every track and still be in the "safe zone". Also what will be the role of LUFS normalization in many streaming services?

Excellent question. I have a post and extension to the spreadsheet for this in the works. Stay tuned.

2) Many popular eq presets (autoeq, @oratory1990, etc..) will require to use a negative gain to avoid clipping. This will often negativaly impact the LUFS so I suppose that it will be hard to understand how to compensate the values in the spreadsheet.

Another excellent point. This is one use-case the "Headroom [dB]" parameter in the spreadsheet is for.
Setting this to 0 means there is zero attenuation in your playback chain. Increase this accordingly.

For example: Let's say you have a headphone with anemic bass and you need to boost it by 3 dB. So you add a +3 dB low-shelf EQ filter and attenuate everything by 4 dB to prevent clipping and also add 1 dB of digital headroom.
In this case you should set the headroom to +4 dB.

There could also be attenuation in other parts of your chain: Let's say you have a separate DAC and amp setup. The DAC volume is set to a fixed -1 dB volume setting (again as digital headroom for peaks), because you control volume only through the amp.
In this case you should increase the headroom and set it to +5 dB.

In the spreadsheet, the headroom will increase the required min amp gain and also the volume setting.
It does not change voltage/current/power requirements because the sensitivity is assumed to be "correct". This would not be the case if, for example, sensitivity was measured at 1 kHz but the headphones' FR had a dip at 1 kHz.

 

[Soundescape]

Another excellent point. This is one use-case the "Headroom [dB]" parameter in the spreadsheet is for.
Setting this to 0 means there is zero attenuation in your playback chain. Increase this accordingly.

Yes I supposed that it was that cell but I still have some doubt that we can simply translate the negative pre-gain of EQ in the headroom value as is.
It is hard to know from presets, without any other calculation, how the LUFS is impacted. I suppose that in the headroom we need to compensate the LUFS as if we consider just a potential peak (dBTP) we have always 0 headroom also with EQ presets.

 

[xnor]

Perception of loudness, BS-1770
So far, I've avoided talking about perception of loudness. Why? A-weighting is a horrible weighting filter after all, right? It's been chosen seemingly arbitrarily and is based on 40-phon equal loudness contours which means it's valid for the perception of loudness of single tones at very low SPL. So this is all invalid?

No, there are good reasons for this:

• This is about using an established reference for hearing loss and not perception of loudness.
• A-weighting was used in the hearing loss research that EPA/NIOSH limits/recommendations are based on.
• A-weighted total RMS amplitude is very easy to measure/implement.
• A-weighting is readily available in SPL meters, making it easy to do your own measurements and compare the numbers.
• A-weighting is "ok" even though it attenuates 20 Hz by 50 dB for reasons explained in #10.

When it comes to perception of loudness, there is an established standard called ITU-R BS-1770.
The loudness calculation process is a bit more involved.

The weighting filter is called "K-weighting":

There's again a highpass filter, because very low frequency content is mostly irrelevant for perceived loudness, and there's also a boost of high frequencies but it is quite a bit higher (+4 dB) than in A-weighting.

Instead of a single total value, RMS amplitudes are calculated for 400ms windows and averaged. These values are filtered by a gate to eliminate windows that are silent in an absolute sense (below -70 dB) and in a relative sense (over 10 dB drop from one window to the next) because that reflects how our perception of loudness works.
The result has the unit "LKFS" or "LUFS": Loudness, K-weighted, relative to full scale.

The results are normalized such that a ~1 kHz full-scale sine wave will result in -3 LUFS, similar to how a full-scale sine wave will result in a -3 dB total RMS amplitude if A-weighted or unweighted.

Note: While the averaging and gating results in a number that more accurately reflects perceived loudness, it will give incorrect readings for the total (damaging) energy that your hearing receives.

Let's look at the values with my two samples:
Classical: -19.6 LUFS
Modern pop/rock: -8 LUFS
That means the modern pop/rock music is perceived to be 11.6 dB louder than the classical track. That's perceptually over twice as loud.

How does this compare to the total RMS values from #1?
Unweighted, the difference is 12.9 dB.
A-weighted, the difference is 11.85 dB.

As you can see, the difference in A-weighted total RMS value between my tracks is actually quite close to their difference in perceived loudness.



ReplayGain aka loudness equalization
ReplayGain is old technology that I've used for many, many years. It's the only technology that is an effective weapon against the loudness war (ever and ever increasing dynamic-range compression with the goal of increased loudness). Sadly, it took the industry and a lot of audiophiles over a decade to realize this. Luckily, with the standardization of BS-1770 more and more broadcasters and streaming service have started adopting this standard in recent years. This is single-handedly the biggest achievement in digital audio in recent history.

So what does it do? It simply attenuates each track/album according to a loudness measure with the goal of equalizing perceived loudness across all tracks/albums, punishing "loud" (low dynamic range) tracks/albums.

So what's the target level? Well, the European Broadcasting Union (EBU) came up with a recommendation based on BS-1770 called EBU R-128 that defines a target level of -23 LUFS.

Given the -19.6 LUFS for the classical sample, this would mean an additional attenuation of 3.4 dB and 15 dB attenuation for the modern rock/pop track.
Obviously, this huge drop in volume creates problems for a lot of consumers and their systems, so different audio players and streaming services have adopted higher target levels:

Tidal, Amazon Music, YouTube, Spotify:
-14 LUFS

Apple Music:
-16 LUFS

ReplayGain (like implemented in Foobar2000):
-18 LUFS

For example, if you listen to the modern pop/rock track on Tidal, Amazon, YouTube or Spotify, there's an additional digital attenuation of 6 dB. That's -6 dB.
The classical track on the other hands needs to be boosted by +5.6 dB.

Wait.. what? How can a player boost the classical track that has sample peaks near 0 dBFS by nearly ~6 dB? It' cant, except if you accepted an extreme amount of clipping or engaged dynamic range compression.
That's the tradeoff that these services made: the higher target level results in less attenuation but it also means that silent tracks cannot be properly loudness-equalized.


Conclusion
In the spreadsheet, add +6 dB to headroom when you're listening to modern pop/rock on Tidal, Amazon, YouTube or Spotify.
For my classical sample, you're out of luck because the player would need to boost by 5.6 dB beyond full-scale.

For Apple Music, add +8 dB to headroom for modern pop/rock instead.
For classical, you're again out of luck. You either need dynamic range compression (which will change the total RMS amplitude) or simply accept the lower perceived loudness.

For ReplayGain, add +10 dB to headroom for modern pop/rock instead.
For classical, you're again out of luck, but the gap in perfectly equalized loudness has reduced to only 1.6 LU (= Loudness Unit = dB) which is negligible.

Depending on the player, you might be able to turn down the volume by these boosts and shift the target down to -19.6 LUFS that way, resulting in 0 dB boost for the classical track. In the spreadsheet simply add the additional attenuation as additional headroom.

 

[xnor]

In Foobar2000, after scanning a file you can view the track gain in the file Properties - ReplayGain window. This "track gain" is to be understood as LU (relative dB):

For my modern pop/rock example it says -10 dB. This means the track loudness is -8 LUFS and it needs to be attenuated by 10 dB to reach the -18 LUFS target.

ReplayGain (RG) can be configured in the preferences:


With the settings in the screenshot,

1. Source mode: Each album is processed as if it was a single track, preserving the loudness differences between individual tracks while equalizing loudness across albums.
   This prevents e.g. deliberately silent intro/outro tracks on an album to be massively boosted in volume.
   
   
2. Processing: Gains are applied in a best-effort mode up to to the clipping point.
   For example, if a track would need to be boosted by 3 dB but it contains sample peaks at -1 dBFS then it would only be boosted by 1 dB.
   
   
3. Preamp: Tracks with RG info get an additional +4 dB boost.
   This effectively raises the loudness target from -18 to -14 LUFS to match Tidal, Amazon, YouTube or Spotify.
   
   
4. Preamp: Tracks without RG info get attenuated by 6 dB.
   Since we've configured a loudness target of -14 LUFS, files that we haven't scanned yet will be attenuated by 6 dB. This is based on the assumption that new files might be highly compressed and -8 LUFS loud, so 6 dB of attenuation would bring them down to -14 LUFS.

Obviously, if you configure your player that way you need to lower the additional headroom in the spreadsheet accordingly.

 

[F1308]

Heya,

there's a couple of threads asking about safe listening levels and people asking about voltage/power requirements in almost any amp/headphone thread.
Here's my take on this:


Noise Exposure Limits
The EPA and WHO recommend that noise should be kept below 70 dBA over 24 hours and below 75 dBA over 8 hours. Additionally, the CDC makes the rough recommendation to keep noise exposure below 2 hours for 80-85 dBA loud noise as (based on the same data and 3 dB exchange rate) to prevent hearing damage.

NIOSH defines a 3 dB exchange rate: permissible exposure time halves for every 3 dB increase in noise intensity.
NIOSH recommends a limit of occupational noise exposure to 85 dBA over an 8-hour time-weighted average.
EPA recommends noise exposure to be limited to 85 dBA over 45 minutes.
View attachment 233575

Why this discrepancy? The answer is in the:


Fine print
The EPA limits were chosen to protect 96% of the general population against impairment of physical (hearing loss) and mental (like discomfort) health.
The NIOSH limits were chosen solely to protect against hearing loss in the workplace accepting that 8% of the workforce will still develop hearing loss.
Therefore, NIOSH recommends hearing protection if noise levels exceed 85 dBA regardless of exposure duration.

The EPA limit is averaged over 24 hours.
The NIOSH limit is averaged over 8 hours (average workday) with rest/recovery periods between exposures.

The EPA limit is based on 365 days/year exposure.
The NIOSH limit is based on 250 workdays/year exposure.

The NIOSH limit considers implementation cost for businesses to stay within limits (sacrificing human health for economic reasons).

Note: both recommendations are based on audiometric tests of hearing loss up to 4 kHz.
Note: OSHA (which records occupational hearing loss cases) defines a significant decrease in hearing as a "standard threshold shift" which is a change of 10 dB averaged over 2, 3, and 4 kHz.


A-Weighting
A-weighting significantly attenuates low frequencies, while giving a slight boost to frequencies between 1 kHz and 6 kHz (the peak is about +1.3 dB at 2.5 kHz):
View attachment 233555


Conclusions
85 dBA should not be considered a universally safe limit, especially not for children, people with sensitive hearing, when regularly listening for several hours, or when being exposed to other potentially louder noise sources throughout the day.
Therefore, I recommend to stay below 85 dBA when listening to music.



Power/Voltage Requirements
This depends on headphone sensitivity and type of music you're listening to:


Headphone sensitivity
You can find this in product datasheets. If it's just specified as "x dB" then it is usually at 1 mW. Sensitivity is sometimes also specified at 1 Vrms.
Both are typically measured with a 500 Hz or 1 kHz sine wave.

To convert from dB SPL@1 mW to dB SPL@1 Vrms and vice-versa, calculate:

sensitivity_Vrms = sensitivity_mW - 10*log10(0.001 * impedance)
sensitivity_mW = sensitivity_Vrms + 10*log10(0.001 * impedance)

Note that a sine wave's RMS value is 3 dB lower than its peak magnitude. This needs to be considered when we analyze the RMS value of music tracks.
Additionally, we have to apply the A-weighting.


Music
Let's look at two extremes: classical recordings and highly dynamic range compressed modern pop/rock.
Note: the selection of tracks used for this analysis is random. Ymmv.


Classical:
View attachment 233576
Total RMS value: -24.1 dB
Total RMS value with A-weighting: -26.85 dB.

Modern pop/rock
View attachment 233581

Total RMS value: -11.2 dB
Total RMS value with A-weighting: -15 dB.

The differences in A-weighting (-2.75 dB for classical and -3.8 dB for modern pop/rock) is explained due to the fact that modern pop/rock has significantly more energy in bass/lower mids and also upper treble, which is exactly what the A-weighting filter attenuates.


So how much power/voltage do I need?
Now we have all the information we need:

• The target SPL: 85 dB SPL
• Sensitivity in dB SPL either @1 mW or @1 Vrms
• Weighted total RMS value

Note: for a 1 kHz sine wave, the weighted total RMS value would be -3 dB, hence the need to subtract an extra 3 dB from the target SPL.

power_mW = 10^((target_spl - sensitivity_mW - weighted_rms - 3)/10) voltage_rms = 10^((target_spl - sensitivity_Vrms - weighted_rms - 3)/20)


Amplifier gain, volume setting and headroom
Knowing the required voltage and the output voltage of your source device, calculating the required gain with optional added headroom is as simple as:

headroom_x = 10^(headroom_dB/20)
min_amp_gain_x = voltage_rms/source_rms * headroom_x
min_amp_gain_dB = 20*log10(min_amp_gain_x)

The actual gain of your amp may be higher, which means you'll have to turn down the volume. By how much? Calculate:

volume_x = min_amp_gain_x / amp_gain_x
volume_dB = 20*log10(volume_x)

I've also published a Headphone power spreadsheet that contains these calculations. Feel free to clone/download it.




Sources

1. CDC. What Noises Cause Hearing Loss?. https://www.cdc.gov/nceh/hearing_loss/what_noises_cause_hearing_loss.html
2. EPA [1974]. Information on levels of environmental noise requisite to protect public health and welfare with adequate margin of safety. EPA/ONAC 550/9-74-004. http://nepis.epa.gov/Exe/ZyPDF.cgi/2000L3LN.PDF?Dockey=2000L3LN.PDF
3. NIOSH [1998]. Criteria for a recommended standard: occupational noise exposure. DHHS (NIOSH) Publication Number 98-126. https://www.cdc.gov/niosh/docs/98-126/

Lovely, many thanks.

But it turns out I tested along the week two IEMs: ZERO, rated at 117.5dB/Vrm@1KHz, impedance 10 Ohm +/-15% and SALNOTES, rated at 108 dB/V@ 1KHz, impedance 32 Ohm.

To get the same loudness I set the master volume of my synthesizer at 12 for loudspeaker monitoring, at 1 for the Zero and at 11 for the Salnotes. Always though it would be exactly the opposite, 11 for the Zero and 1 for the Salnotes.

Can you help me understand it ????
Is it that the impedance is involved...?

Thank you.

 

[solderdude]

When looking at efficiency numbers (dB/mW) the impedance is involved.
When looking at sensitivity (dB/V) it is not.... that is ... IF we have a source with near 0 ohm output resistance * and assuming the source in question is not current limited # and assuming the FR is the same ~ or very, very similar.

* When the output resistance is above say... 1 ohm or so (many interfaces and music instruments are, phones etc are not) then there is voltage division at play.
Say we have a 10 ohm output R and 2 headphones with the exact same sensitivity (dB/V) but one is 10 ohm and the other one is 32 ohm.
On a low output R source they will play equally loud (assuming FR is the same as well).
On a 10 ohm output R the 10ohm headphone will be playing 6dB softer and the 32 ohm headphone will play 2.4dB softer.

So in the end, not only sensitivity matters but also impedance combined with output resistance of the source.

# When a source is current limited (most are) there can be a difference in max SPL that can be reached.
When 2 headphones have the same sensitivity (dB/V) and the same FR but one is say... 12 ohm and the other one 300 ohm and the source is used that can supply 10V (in 300 ohm) but only 30mA then the 300 ohm headphone can reach 10V but the 16 ohm headphone can only reach 0.5V that is a whopping 26dB difference in max output level as the dB/V would be the same.
So... max output power in specific impedances also plays a role when looking for max. SPL

~ When a headphone is listed as having say 105dB/V then this is only valid at a specific frequency or frequency band. This depends on the measurement method.
It could be at 400Hz, at 1kHz or even averaged over a narrow band noise. Usually this is not specified.
A headphone with 105dB/V could well have 120dB/V in the bass (very bassy headphone) or be 95dB at 30Hz (bass-light headphone).
Of course with the right EQ you can effectively change the FR to flat or a specific target. When done digital and applying a boost you will need negative pre-amp.