B&O Tech: How loud are my headphones?

 

As you may already be aware, Bang & Olufsen makes headphones: the BeoPlay H6 over-ear headphones and the BeoPlay H3 earbuds.

If you read some reviews of the H6 you’ll find some reviewers like them very much and say things like  “…excellent clarity and weight, well-defined bass and a sense of openness and space unusual in closed-back headphones. The sound is rich, attractive and ever-so-easy to enjoy.” and “… by no means are these headphones designed only for those wanting a pounding bass-line and an exciting overall balance: as already mentioned the bass extension is impressive, but it’s matched with low-end definition and control that’s just as striking, while a smooth midband and airy, but sweet, treble complete the sonic picture.” (both quotes are from Gramophone Magazine’s April 2014 issue). However, some other reviewers say things like “My only objection to the H6s is their volume level is not quite as loud as I normally would expect.” (A review from an otherwise-satisfied on Amazon.com). And, of course, there are the people whose tastes have been influenced by the unfortunate trend of companies selling headphones with a significantly boosted low-frequency range, and who now believe that all headphones should behave like that. (I sometimes wonder if the same people believe that, if it doesn’t taste like a Big Mac, it’s not a good burger… I also wonder why they don’t know that it’s possible to turn up the bass on most playback devices… But I digress…)

For this week’s posting, I’ll just deal with the first “complaint” – how loud should a pair of headphones be able to play?

 

Part 1: Sensitivity

One of the characteristics of a pair of headphones, like a passive loudspeaker, is its sensitivity. This is basically a measurement of how efficient the headphones are at converting electrical energy into acoustical output (although you should be careful to not confuse “Sensitivity” with “Efficiency” – sensitivity is a measure of the sound pressure level or SPL output for the voltage at the input whereas efficiency is a measure of the SPL output for the power in milliwatts). The higher the sensitivity of the headphones, the louder they will play for the same input voltage.

So, if you have a pair of headphones that are not very sensitive, and you plug them into your smartphone playing a tune at full volume, it might be relatively quiet. By comparison, a pair of very sensitive headphones plugged into the same smartphone playing the same tune at the same volume might be painfully loud. For example,let’s look at the measured data for three not-very-randomly selected headphones at http://www.innerfidelity.com/headphone-data-sheet-downloads

 

Brand Model Vrms to produce 90 dB SPL dBV to produce 90 dB SPL
Sennheiser HD600  0.230 -12.77
BeoPlay H6 0.044 -27.13
Etymotic ER4PT  0.03 -30.46

 

If we do a little math, this means that, for the same input voltage, the Etymotic’s will be 3.3 dB louder than the H6’s and the Sennheiser’s will be 14.4 dB quieter. This is a very big difference. (The Etymotic’s are 7.7 times louder than the Sennheisers!)

So, in other words, different headphones have different sensitivities. Some will be quieter than others – some will be louder.

Side note: If you want to compare different pairs of headphones for output level, you could either look them up at the innerfidelity.com site I mentioned above, or you could compare their data sheet specifications using the Sensitivity to Efficiency converter on this page.

The moral of this first part of the story is that, when someone says “these headphones are not very loud” – the question is “compared to what?”

 

Part 2: The Source

I guess it goes without saying, but if you want more out of your headphones, the easiest solution is to turn up the volume of your source. The question then is: how much output can your source deliver? This answer also varies greatly from product to product. For example, if I take four not-very-randomly selected measurements that I did myself, I can see the following maximum output levels for a 500 Hz,  0 dB FS sine tone at maximum volume sent to a 31 ohm load (a resistor pretending to be a pair of headphones):

 

Brand Model Vrms dBV
Lenovo ThinkPad T420 0.317 -9.98
Apple iPhone 3Gs 0.89 -1.01
Apple MacBookPro 2.085 +6.38
Sony CDP-D500 6.69 16.51

 

In other words, the Sony is more than 26 dB (or 21 times) louder than the ThinkPad, if we’re just measuring voltage. This is a very big difference.

So, as you can see, turning the volume all the way up to 11 on different product results in very different output levels. This is even true if you compare iPod Nano’s of different generations, for example – no two products are the same.

The moral of the story here is: if your headphones aren’t loud enough, it might not be the headphones’ fault.

 

Part 3: The Details, French Law, and How to Cheat

So much for the obvious things – now we are going to get a little ugly.

Let’s begin the ugliness with a little re-hashing of a previous posting. As I talked about in this posting, your ears behave differently at different listening levels. More specifically, you don’t hear bass and treble as well when the signal is quiet. The louder it gets, the more flat your “frequency response”. This means that, when acoustical consultants are making measurements of quiet things, they usually have to make the microphone signal as “bad” as your hearing at low levels. For example, when you’re measuring air conditioning noise in an office space, you want to make your microphone less sensitive to low frequencies, otherwise you’ll get a reading of a high noise level when you can’t actually hear anything. In order to do this, we use something called an “weighting filter” which is an attempt to simulate your frequency response. There are many different weighting curves – but the one we’ll talk about in this posting is an “A-weighting” curve. This  is a filter that attenuates the low and high frequencies and has a small boost in the mid-band – just like you do at quiet listening levels. The magnitude response of that curve is shown below in Figure 1. At higher levels (like measuring the noise level at the end of a runway while a plane is taking off over your head), you might want to use a different weighting curve like a “C-weighting” filter – or none at all.

The magnitude response of an A-weighting filter.
Fig 1. The magnitude response of an A-weighting filter.

 

So, let’s say that you get enough money on Kickstarter to create the Fly-by-Night Headphone Company and you’re going to make a flagship pair of headphones that will sweep the world by storm. You do a little research and you start coming across something called “BS EN 50332-1” and “BS EN 50332-2“. Hmmmm… what are these? They’re international standards that define how to measure how loudly a pair of headphones plays. The procedure goes something like this:

  1. get some pink noise
  2. filter it to reduce the bass and the treble so that it has a spectrum that is more like music (the actual filter used for this is quite specific)
  3. reduce its crest factor so your measurement doesn’t jump around so much (this basically just gets rid of the peaks in the signal)
  4. do a quick check to make sure that, by limiting the crest factor, you haven’t changed the spectrum beyond the acceptable limits of the test procedure
  5. play the signal through the headphones and measure the sound pressure level using a dummy head
  6. apply an A-weighting to the measurement
  7. calculate how loud it is (averaged over time, just to be sure)

So, now you know how loud your headphones can play using a standard measurement procedure. Then you find out that, according to another international standard called EN 60065 or EN 60950-1 there are maximum limits to what you’re permitted to legally sell… in France… for now… (Okay, okay, these are European standards, but Europe has more than one country in it, so I think that I can safely call them international…)

So, you make your headphones, you make them sound like you want them to sound (I’ll talk about the details of this in a future posting), and then you test them (or have them tested) to see if they’re legal in France. If not (in other words, if they’re too sensitive), then you’ll have to tweak the sensitivity accordingly.

 

Okay – that’s what you have to do – but let’s look at that procedure a little more carefully.

Step 1 was to get some pink noise. This is nothing special – you can get or make pink noise pretty easily.

Step 2 was to filter the noise so that its spectrum ostensibly better matches the average spectrum of all recorded and transmitted music and speech in the world. The details of this filter are in another international standard called IEC 60268-1.  The people who wrote this step mean well – there’s no point in testing your headphones with frequencies that are outside the range of anything you’ll ever hear in them. However, this means that there is probably some track somewhere that includes something that is not represented by the spectral characteristics of the test signal we’re using here. For example: Figure 2, below shows the spectral curve of the test signal that you are supposed to send to the headphones for the test.

The magnitude response of the filter applied to the pink noise before sending it to the headphones.
Fig 2. The magnitude response of the filter applied to the pink noise before sending it to the headphones.

 

Compare that to Figure 3, which shows an analysis of a popular Lady Gaga tune that I use as part of my collection of tunes to make a woofer unhappy. This is a commercially-available track that has not been modified in any way.

The spectrum of a Lady Gaga tune. Compare this with the noise filter plot from Figure 2 (plotted in red for your convenience).
Fig 3. The spectrum of a Lady Gaga tune. Compare this with the noise filter plot from Figure 2 (plotted in red for your convenience).

As you can see, there is more energy in the music example than there is in the test signal around the 30 – 60 Hz octave – particularly noticeable due to the relative “hole” in the response that ranges between about 70 and 700 Hz.

Of course, if we took LOTS of tunes and analysed them, and averaged their analyses, we’d find out that the IEC test signal shown in Figure 2 is actually not too bad. However, every tune is different from the average in some way.

So, the test signal used in the EN 50332 test is not going to push headphones as hard as some kinds of music (specifically, music that has a lot of bass content),

We’ll skip Step 3, Step 4, and Step 5.

Step 6 is a curiosity. We’re supposed to take the signal that we recorded coming out of the headphones and apply an A-weighting filter to it. Now, remember from above that an A-weighting filter reduces the low and high frequencies in an effort to simulate your bad hearing characteristics at quiet listening levels. However, what we’re measuring here is how loud the headphones can go. So, there is a bit of a contradiction between the detail of the procedure and what it’s being used for. However, to be fair, many people mis-use A-weighting filters when they’re making noise measurements. In fact, you see A-weighted measurements all the time – regardless of the overall level of the noise that’s being measured. One possible reason for this is that people want to be able to compare the results from the loud measurements to the results from their quiet ones – so they apply the same weighting to both – but that’s just a guess.

 

Let’s, just for a second, consider the impact of combining Steps 2 and 6. Each of the filters in both of these steps reduce the sensitivity of the test to the low and high frequency behaviour of the headphones. If we combine their effects into a single curve, it looks like the one in Figure 4, below.

The magnitude response of the combination of the A-weighting filter and the filter applied to the pink noise signal.
Fig 4. The magnitude response of the combination of the A-weighting filter and the filter applied to the pink noise signal.

 

At this point, you may be asking “so what?” Here’s what.

Let’s take two different pairs of headphones and pretend that we measured them using the procedure I described above. The first pair of headphones (we’ll call it “Headphone A”) has a completely flat frequency response +/- < 0.000001 dB from 20 Hz to 20 kHz. The second pair of headphones has a bass boost such that anything below about 120 Hz has a 20 dB gain applied to it (we’ll call that “Headphone B”). The two unweighted measurements of these two simulated headphones are shown in Figure 5.

The magnitude responses of the two simulated headphones. The blue curve is "Headphone A". The red curve is "Headphone B".
Fig 5. The magnitude responses of the two simulated headphones. The blue curve is “Headphone A”. The red curve is “Headphone B”.

 

After filtering these measurements with the weighting curves from Steps 2 and 6 (above), the way our measurement system “hears” these headphone responses is slightly different – as you can see in Figure 6, below.

The magnitude responses of the two simulated headphones as "seen" by a EN 50332 measurement. The blue curve is "Headphone A". The red curve is "Headphone B".
Fig 6. The magnitude responses of the two simulated headphones as “seen” by a EN 50332 measurement. The blue curve is “Headphone A”. The red curve is “Headphone B”.

 

So, what happens when we measure the sound pressure level of the pink noise through these headphones?

Well, if we did the measurements without applying the two weighing curves, but just using good ol’ pink noise and no messin’ around, we’d see that Headphone B plays 13.1 dB louder than Headphone A (because of the 20 dB bass boost). However, if we apply the filters from Steps 2 and 6, the measured difference drops to only 0.46 dB.

This is interesting, since the standard measurement “thinks” that a 20 dB boost in the entire low frequency region corresponds to only a 0.46 dB increase in overall level.

 

Figure 7 shows the relationship between the bass boost applied below 120 Hz and the increase in overall level as measured using the EN 50332 standard.

The relationship between the increase in SPL as measured using the EN 50332 standard vs. the gain of a bass boost applied to the headphones. (filter characteristics are Low shelving, fc=120 Hz, Q=0707)
Fig 7. The relationship between the increase in SPL as measured using the EN 50332 standard vs. the gain of a bass boost applied to the headphones. (filter characteristics are Low shelving, fc=120 Hz, Q=0.707)

 

So, let’s go back to you, the CEO of the Fly-by-Night Headphone Company. You want to make your headphones louder, but you also need to obey the law in France. What’s a sneaky way to do this? Boost the bass! As you saw above, you can crank up the bass by 20 dB and the regulators will only see a 0.46 dB change in output level. You can totally get away with that one! Some people might complain that you have too much bass in your headphones, but hey – kids love bass. And plus, your competitors will get complaints about how quiet their headphones are compared to yours. All because people listening to children’s records at high listening levels hear much more bass than the EN 50332 measurement can!

Of course, one other way is to just ignore the law and make the headphones louder by increasing their sensitivity… but no one would do that because it’s illegal. In France.

 

 

Appendix 1: Listen to your Mother!

My mother always told me “Turn down that Walkman! You’re going to go deaf!” The question is “Was my mother right?” Of course, the answer is “yes” – if you listen to a loud enough sound for a long enough time, you will damage your hearing – and hearing damage, generally speaking, is permanent.  The louder the sound, the less time it takes to cause the damage. The question then is “how loud and how long?” The answer is different for everyone, however you can find some recommendations for what’s probably safe for you at sites that deal with occupational health and safety. For example, this site lists the Canadian recommendations for maximum exposure time limits to noise in the workplace. This site shows a graph for the US recommendations for the same thing – I’ve used the formula on that site to make the graph in Figure 8, below.

 

Recommendations for the maximum time of exposure to noise sources according to The National Institute for Occupational Safety and Health (NIOSH) in the USA.
Fig 8. Recommendations for the maximum time of exposure to noise sources according to The National Institute for Occupational Safety and Health (NIOSH) in the USA.

 

 

How do these noise levels compare with what comes out of my headphones? Well, let’s go back to the numbers I gave in Part 1 and Part 2. If we take the measured maximum output levels of the 4 devices listed in Part 2, and calculate what the output level in dB SPL would be through the measured sensitivities of the headphones listed in Part 1 (assuming that everything else was linear and nothing distorted or clipped or became unhappy – and ignoring the fact that the headphones do not have the same impedance as the one I used to do the measurements of the 4 devices… and assuming that the measurements of the headphones are unweighted on that website), then the maximum output level you can get from those devices are shown in Figure 9.

 

Calculated maximum output levels in dB SPL for the four devices and three headphones listed in Parts 1 and 2, above.
Fig 9. Calculated maximum output levels in dB SPL for the four devices and three headphones listed in Parts 1 and 2, above. Blue is the Etymotic ER4PT, red is the BeoPlay H6, and black is the Sennheiser HD600.

 

So, if you take the calculations shown in Figure 8 and compare them to the recommendations shown in Figure 7, then you might reach the conclusion that, if you set your volume to maximum (and your tune is full-band pink noise mastered to a constant level of  0 dB FS, and we do a small correction for the A-weighting based on the assumption that the 90 dB SPL headphone measurements listed above are unweighted ), then the maximum recommended time that you should listen to your music, according to the federal government in the USA is as shown in Figure 10.

 

Recommended maximum exposure time for 3 different headphones connected to 4 different sources playing at maximum volume.
Fig 10. Recommended maximum exposure time for 3 different headphones connected to 4 different sources playing at maximum volume (based on a large number of assumptions that may or may not be correct).

 

So, if I only listen to full-bandwidth pink noise at 0 dB FS at maximum volume on my MacBook Pro over my BeoPlay H6’s, then the American government thinks that after 0.1486 of a second, I am damaging my hearing.

It seems that my mother was right.

 

Appendix 2: Why does France care about how loud my headphones are?

This is an interesting question, the answer to which makes sense to some people, and doesn’t make any sense at all to other people – with a likely correlation with your political beliefs and your allegiance to the Destruction of the Tea in Boston. The best answer I’ve read was discussed in this forum where one poster very astutely point out that, in France, the state pays for your medical care. So, France has a right to prevent the French from making themselves go deaf by listening to this week’s top hit on Spotify at (literally) deafening levels. If you live in a place where you have to pay for your own medical care, then you have the right to self-harm and induce your own hearing impairment in order to appreciate the subtle details buried within the latest hip-hop remix of Mr. Achy-Breaky Heart’s daughter “singing” Wrecking Ball while you’re riding on a bus. In France, you don’t.

Appendix 3: Additional Reading

ISVR Consulting’s page

Rodhe and Schwarz’s pdf manual for running the EN 50332 test on their equipment

 

  1. I understand you were also on the design team of H8. It’s a good product (in term of sound) except for Bluetooth connectivity. My HTC H8 phone never work good with it, so I use it with wire.
    Maybe you were not responsible for connectivity but I think it’s way beyond standards of B&O, and no one have a good answer for this issue.

  2. Hi Hadi,

    I helped with the sound design of the H8 – but this means my work was purely acoustical. Consequently, unfortunately, I can’t respond to your comments regarding the Bluetooth connectivity – but I will pass them on to the part of the team responsible for this.

    Cheers
    -geoff

  3. Thanks for this article. But I am still confused:
    ‘How loud does your headphone play?’ Is answered in the first place with the sensitivity figure which is not measured with pink noise, but at 500 Hz (it seems to me as I see this 500 Hz with a lot of manufacturers, just one using 1 kHz instead). This spec, no matter as given in dB/mW or dB/V, is based on the procedure outlined in IEC 60268, and ist most probably also the base for your comparison table of the three headphones.

    > “BS EN 50332-1” and “BS EN 50332-2“. Hmmmm… what are these? They’re international standards that define how to measure how loudly a pair of headphones can play.

    Is that wrong wording? I don’t see how the maximum loudness of a phone is specified with the procedure that you explain. Instead it seems to be a different way to define the sensitivity.

  4. Hi Techland,

    You’re right – my choice of wording is incorrect. The BS standards define a measurement of “how loudly a pair of headphones plays” with a given input signal. I’ll correct this.

    As far as I know, there is no method of defining the maximum output level of a headphone, since we would all have to agree on an acceptable amount of distortion that would define what “maximum” means.

    There is a danger in using a single frequency for defining the sensitivity of anything, since it is unlikely that a total magnitude response of a system is completely flat. If, for example, you have a pair of headphones (or a headphone / measurement coupling) that has a deviation (say, a notch in the magnitude response) at the measurement frequency (say, 1 kHz), then the sensitivity measurement at that one frequency will not be representative of the behaviour of the headphones. Although many manufacturers do define their sensitivity at a single frequency, this cannot be trusted – even if it’s based on an international standard.

    This last statement brings me to the REAL point of my posting. It was not to explain how to test headphones. This is done very well in the standards themselves. My point was to show that a standard isn’t necessarily representative of a useful thing in real life – and if you are reasonably well-informed about real life, you can easily wiggle your way around the standard.

    As John Godfrey Saxe said: “Laws, like sausages, cease to inspire respect in proportion as we know how they are made.” Standards are very similar… :-)

    Cheers
    -geoff

  5. Hello Geoff, and a happy new year!

    I don’t have the ‘BS’ standards, I only have the IEC6026. In that one maximum input power is defined with pink noise, while sensitivity is defined by a 500 Hz sine.

    I completely understood your article but am on the search for some more specific information. AFAI read in the web, the EU regulations limit the max output voltage on portable players, phones etc. to 150 mV. This can not be true, as an EU iPhone will deliver -3.7 dBu = 506 mV. The US version delivers +2.2 dBu = roughly 1 V. Do you have exact information about the allowed max output voltage?

    Another thing from the web: the EU also said that the combination of player and phones is not allowed to exceed 85 dBA SPL in general, and up to 100 dBA SPL, which is said to be the reason we in the EU have a lower output level than the US. And an even more low one if one not deactivates the ‘max volume’ option in the iPhone settings (another 6 dB or so down). Are these EU SPL numbers correct?

    Finally another question that you might be able to answer (sorry for mentioning a competitor’s product): There are rumours that JVC lowered the max SPL of its HA-SZ2000 headphone so it meets EU regulations. The version sold here is called 2000-E and indeed includes 2 resistors and one capacitor, bringing the overall volume down by about 3 dB.

    As I don’t have and know all these regulations I would like to find out if there is any truth in this, or if it is complete rubbish. As you write above the max volume of a phone isn’t even clearly defined and never given by manufacturers, so I have the impression that this JVC mod might have a different reason.

  6. There is still a big volume difference between H8 on Bluetooth and cable. Why is that?

  7. Hi Axel,
    I’ve decided to make the answer to your question the topic of my next blog posting. Hope that’s okay. I should have it done by mid-week.
    Cheers
    -geoff

Leave a Reply