# Headphones sensitivity vs needed power for bass

#### Karister

##### Member
Hi,

Headphones sensitivity is usually (always?) specified for 1kHz frequency. It is usually said that most power is needed for bass reproduction. Why? Can I calculate how much power is needed? Let's say headphones are rated at 90dB/mW. Providing 1mW of power them will produce 90dB sound which is quite loud. How does it work for bass? Is it somehow connected to human hearing which is worse for low frequencies and (according to isophones) bass needs to be boosted significantly in dB to be perceived at the same level and thus we need more power? Or is it something else?

#### Vini darko

##### Active Member
A simple way to explain the extra power needed for bass is. The amplifier has to move the driver physically further then stop it and make it move further in the other direction. You can try this with a heavy object like a brick. Try moving it fast a tiny amount forwards and backwards, pretty easy. Then try moving it several feet fast, forwards and backwards requires a lot more energy. Particularly to stop it and make it return.

OP

#### Karister

##### Member
But why further? If I am not mistaken, further excursion of driver produces bigger wave amplitude which means more SPL and louder sound. Let's say again we have a headphone rated at 90dB/mW. Amplifier produces voltage, headphone has resistance and some current is flowing delivering power. Let's say 1mW. So this headphone will play 1kHz at 90dB using this power. Will it play 20Hz at 90dB using 1mW of power as well? If so, why does driver have to move further for reproducing bass than mid tones?

The only idea that comes to my mind is one from my previous post - human hearing is less sensitive for bass. So when I listen to 1kHz at 60dB, 40Hz needs to be played at 80dB to be perceived same as loud. This 20dB means 100 times more power needed. But this is just my guess. I could be wrong about producing the same SPL from 1mW at each frequency. Or it could be both reasons. I am looking either for confirmation or negation with explanation.

#### Fluffy

##### Addicted to Fun and Learning
I do believe this should be reflected in the headphones frequency response. if it rolls off at the bass frequencies relative to 1khz, then it indeed needs more power to generate a signal with the same SPL at in the bass. in closed headphones its sometimes the other way around – the bass is boosted massively so I think it would mean they are more efficient in the bass area.

#### Aerith Gainsborough

##### Active Member
But why further? If I am not mistaken, further excursion of driver produces bigger wave amplitude which means more SPL and louder sound.
You do realize that you need to move more air the lower you get in the frequency to achieve the same SPL?

Ah found the article:
https://www.audioholics.com/loudspeaker-design/audibility-of-distortion-at-bass

Simple experiment: play 1KHz @90dB and watch the driver of your speaker. You won't see anything.
Now try to play 20Hz at the same SPL and watch what happens.

Disclaimer: Don't. Unless it's a sub you'll probably damage the driver. Instead, gradually ramp up the volume while measuring the SPL, you'll see soon enough what I mean.

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#### Vini darko

##### Active Member
Impedance and frequency response of a transducer is also a reason power requirements change with spl over frequency.

OP

#### Karister

##### Member
You do realize that you need to move more air the lower you get in the frequency to achieve the same SPL?
Actually I was missing this one. Thanks. I saw driver of my sub moving many times but I always thought it is due to producing more SPL than rest of the speakers. I was unaware that low frequencies requires more air moved to produce the same SPL. This chart looks very informative. Is there a formula that allows to calculate it freely for other values?
My ultimate goal is to be able determine how much power is needed for bass reproduction at equal perceived loudness when I know headphone (or speaker) sensitivity at 1kHz. Hearing curves allows me to find required SPL. I know that each +10dB at 1kHz will require ten times the power. I am still missing something to calculate it for lower frequencies.

#### solderdude

##### Major Contributor
You are clearly over-thinking this.
Some headphones have a massive bass boost, others are rolled off.
You need enough power to reach 120dB SPL peak in a headphone and you are done.

Here you can enter the data and get the info you need
Fill in 120dB if you want to play really, really loud

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Forum Donor
OP

#### Karister

##### Member
You are clearly over thinking this.
Some headphones have a massive bass boost, others are rolled off.
You need enough power to reach 120dB SPL peak in a headphone and you are done.

Here you can enter the data and get the info you need
Fill in 120dB if you want to play really, really loud
I know this calc and I agree that I am over thinking it. It is just a pure demand of knowledge. We can assume flat resistance across frequency and flat frequency response. But I still would like to know how to find sensitivity for other frequencies than 1kHz. I assume it will be lower for bass as more air needs to be moved for the same SPL.

#### solderdude

##### Major Contributor
I assume it will be lower for bass as more air needs to be moved for the same SPL.

When it is flat (none really are) and the impedance is flat (some are) then the efficiency in voltage and power is exactly the same for all frequencies.
When bass is boosted, say +5dB oppositie 1kHz then the efficiency is 5dB higher for the lows.
When bass is rolled-off say -5dB oppositie 1kHz then the efficiency is 5dB lower for the lows.
It has absolutely nothing to do with excursion difference.

When a headphone has an impedance bump but is flat in response than the voltage efficiency is the same for all frequencies but power efficiency in the lows is higher (less power needed for the same excursion)

That said, some headphones do have a limited excursion and tend to 'compress' a little at higher SPL (3rd and 5th harm increase) but this is rare.
Some power ratings are very low (20mW) and can be blown up when bass is boosted to the extreme.
Some drivers are known to reach physical excursion limits and touch the magnet assembly at very loud volumes

A lot of headphones are specified at 500Hz and some by using shaped noise. It also depends on what test rig efficiency is measured and there is unit-to-unit variance/tolerance as well. I have measured a few dB between L and R with some headphones.

You have to differentiate between dB SPL and Phon. We hear in Phon. Music is mastered by ear at around 75 to 80dB average levels. In that case the sound should be balanced to our ears. The actual electrical signal and power levels are quite different.
This, however, has nothing to do with efficiency.

Below the spectrum of a typical recording. You can see most of this is lower frequencies. A bit like pink noise spectrum. We hear this as balanced and the transducers (headphones or speakers) have to reproduce each frequency at the same volume (so with the same voltage efficiency).

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OP

#### Karister

##### Member
Thanks. I use HiFiMAN Arya which (according to several reviews) has a pretty flat frequency response in range of 20Hz-1kHz. Not sure about impedance but let's assume it's flat for the sake of simplicity. It is rated at 90dB/[email protected] Would it mean the same efficiency for 20Hz, 100Hz and 1000Hz? I find it against what @Aerith Gainsborough said regarding more air moved and power needed for low bass (in comparison to mids at the same SPL) reproduction. Same efficiency would not mean more power need for bass.

If this is not about excursion, am I right with following:
- let's say again efficiency is 90dB/[email protected]
- bass frequency response is -10dB opposite 1kHz (and flat resistance)
- hearing curves say I need +5dB SPL to have same loudness perceived for bass (I think this solves issue with hearing in phon not SPL)
So do I need 15dB (10dB for headphone bass frequency response and 5dB for compensating hearing curves) more SPL to hear bass same as loud as mid tones in this case?

Sorry but I would really like to understand this.

#### Aerith Gainsborough

##### Active Member
Here you can enter the data and get the info you need
Fill in 120dB if you want to play really, really loud
Haha, this site is fun. Makes is very clear that my Focal Clear is ridiculously easy to drive.

It is rated at 90dB/[email protected] Would it mean the same efficiency for 20Hz, 100Hz and 1000Hz? I find it against what @Aerith Gainsborough said regarding more air moved and power needed for low bass (in comparison to mids at the same SPL) reproduction. Same efficiency would not mean more power need for bass.
I was talking about excursion, not power.
Power needs to take other factors into consideration.
For a simplistic view you can use the frequency response, since the sweep to generate it is applied with the same power at all frequencies.
If you want to calculate it more in depth, you need to take phase angle and impedance into account and these are not that easily understood.

Here you have detailed measurements for the Focal Clear:
https://www.innerfidelity.com/images/FocalClearsnA1BRQE000007.pdf

Look at impedance and phase, they vary by frequency. have fun crunching the numbers. Considering that you have a variation of <2dB between 1KHz and 20Hz, I think doing the math yourself is complete overkill.

Interesting article related to the topic:
https://www.audioholics.com/loudspeaker-design/understanding-impedance-electrical-phase

So do I need 15dB (10dB for headphone bass frequency response and 5dB for compensating hearing curves) more SPL to hear bass same as loud as mid tones in this case?
No. Do not do that. Listen to a flat/neutral transducer at 80ish dB and you hear what the artist intended. If you listen at the same volume as the mastering engineers, most of the human ear's Frequency response is already accounted for and "baked into" the music (with the exception of variations between individuals).

If you lower the volume by 10dB you (rough estimate) lower the volume of the bass by only half that amount in order to compensate for lower listening level and the human ear's lame volume dependent low frequency sensitivity. There are devices and software that do this to some extent, it's called: "Loudness compensation" or simply "Loudness".

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#### solderdude

##### Major Contributor
Thanks. I use HiFiMAN Arya which (according to several reviews) has a pretty flat frequency response in range of 20Hz-1kHz. Not sure about impedance but let's assume it's flat for the sake of simplicity. It is rated at 90dB/[email protected] Would it mean the same efficiency for 20Hz, 100Hz and 1000Hz? I find it against what @Aerith Gainsborough said regarding more air moved and power needed for low bass (in comparison to mids at the same SPL) reproduction. Same efficiency would not mean more power need for bass.

If this is not about excursion, am I right with following:
- let's say again efficiency is 90dB/[email protected]
- bass frequency response is -10dB opposite 1kHz (and flat resistance)
- hearing curves say I need +5dB SPL to have same loudness perceived for bass (I think this solves issue with hearing in phon not SPL)
So do I need 15dB (10dB for headphone bass frequency response and 5dB for compensating hearing curves) more SPL to hear bass same as loud as mid tones in this case?

Sorry but I would really like to understand this.
For the Arya the voltage sensitivity = 104dB/V (90dB/mW)

This is the same for frequencies between 10Hz and 1kHz. From 2kHz to 6kHz the efficiency is about 98dB/V. Around 8kHz the efficiency is around 109dB/V

That is the efficiency part.

The efficiency part has absolutely nothing to do with how the human hearing works (equal loudness contours) nor with the recording and how this was made.
It also has nothing to do with boosting or lowering frequencies using EQ to suit our taste or compensate for efficiency differences.

Phon equal to SPL around 1kHz (and 6kHz) only.
Measurements are only done in SPL. These can have a dertain 'weighting'. The most common is A-weighting as it is somewhat similar to ur hearing at a certain sound level.
We hear in Phon... we measure efficiency in SPL.
At 100 Phon the hearing is 'flat' from 20Hz to 1kHz so at that level Phon = SPL

The amount of energy in recordings (for humans to perceive it as 'flat' is somewhat similar to pink noise. The 'bass boost' thus is NOT in the efficiency but in the recording. It is embedded in the electrical signal.
All the transducers have to do is reproduce each frequency in the same SPL (thus NOT Phon) as it is in the signal.
How loud we perceive the bass (relatively) depends on how loud the average level is.

Recordings are usually made between 75dB and 80dB SPL on average. When you play it back at the same (average, not peak) SPL it will sound balanced. When you play it louder the tonal balance does not change much. It only really becomes a 'thing' when levels drop below 80dB SPL

Again... this has nothing to do with efficiency nor with how much energy there is in low frequencies in the recording.

Now back to the original question as to how much power you need.
Uncomfortable loud levels, which you can listen to for about the duration of a few minutes top, is about 100dB SPL (Phon).
However, as music is dynamic there can be peaks about 5dB to 25dB louder than 100dB.
The 120dB+ peaks are really uncomfortable and will be hard to reach with speakers in a room but can easily be reached by quite a few headphones.

So this means (as dBSPL = Phon above 90dB SPL) your amplifier needs to supply enough voltage to reach 120dB (at 1kHz) when the frequency response is about flat. This has nothing to do with impedance peaks as headphones are voltage driven, not power driver.

In your case 120dB SPL is reached at 6.3V and when you want to build-in some extra headroom you need 12V.
6V in 35 Ohm = 1W
12V in 5 Ohm = 4W

These numbers is where the 'you need tons of power' story comes from. You need it with inefficient headphones when you want to reach more than impressive peak levels for short moments without any distortion of the electrical signal.

Now... do you really need this for listening to music at pleasant levels that one can sustain for a few hours ?
No of course not.
For this average levels are somewhere around 70dB average so peak levels of 90dB can be present.
For this you only need about 0.001 W (1mW) where even a phone can reach 1V = 30mW.

This explains why some folks say.. you don't really need a high amount of power... this or that headphone plays loud enough from a phone.
Calculations, however, say a different thing when you want to reach extreme levels.

This is where the discrepancy comes from.

Basically, for background listening to comfortable loud levels (100dB peaks) a 1V output (30mW) in case of the Arya is enough.
When you want to (shortly) reach impressive levels 1W is enough.
That is the fun of (close to) logarithmic hearing.

To put this in perspective... the Focal Spirit One for instance can reach 120dB at 1V already (30mW as well) so there can be huge differences in efficiency. For that reason you can use lists or the headphonesty calculators for each individual case.

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OP

#### Karister

##### Member
Thanks for all explanations. I usually listen at moderate volumes. Something like human voice during excited talk. Sound level meter says 60-65dB when put as close to headphone as possible. Same reading for listening from my stereo. For all my previous headphones I used to boost 40-60Hz by a few dB. Arya is first one that I do not do that. According to headphonesty calculator my laptop headphone out has enough power ([email protected]) for my listening. I wonder why a lot of audiophiles claim their headphones sound dull without amps offering 5-7W of power. They use Focal Clear and Audeze LCD-2 and other models with sensitivity above 100dB. Sounds like a nonsense.

For some tests I picked few sub bass boosted songs. Schiit Asgard 2 ([email protected]) produced a lot of distortions with my HiFiMAN Arya. At full volume it wasn't unconformably loud for a short period of time but there were easily audible cracks. When plugged into RME ADI 2 DAC FS ([email protected]), I did not managed to go full volume as it became too loud. There were no distortions, though. Would it be due to more power or are there some other factors?

#### solderdude

##### Major Contributor
I wonder why a lot of audiophiles claim their headphones sound dull without amps offering 5-7W of power. They use Focal Clear and Audeze LCD-2 and other models with sensitivity above 100dB. Sounds like a nonsense.
Some of this is nonsense based on 'theories' they have or personal experiences where they did not actually monitor/measure actual power used.
The calculations are clear though. Your headphone needs 1W to reach impressive/authorative levels but when using it to enjoy music in long sessions a phone is all that is needed in praxis.
That is where technically the discrepancies come from.

I can't say what 'cracks' you heard and whether or not the same music /source was used and only the amp differed.

#### Aerith Gainsborough

##### Active Member
Your headphone needs 1W to reach impressive/authorative levels but when using it to enjoy music in long sessions a phone is all that is needed in praxis.
Oddly enough, my Clear does not like my phone at all. I need to really crank it at the phone to get it up to a reasonable level and stuff sounds... flat.
Clear sounds wonderful from my PC Soundcard and even my AVRs headphone out. On my phone, the ATH-M50s I use for outdoor listening sound better.

So I guess it depends on the amp implementation on the respective phone.

As for the audible cracks: sounds like clipping to me.

#### solderdude

##### Major Contributor
Your PC soundcard may have a higher than usual output resistance. The phone will have a very low output resistance.
The M50 has boosted bass and is closed which helps outdoors as well.
There is tone control on the phone so why not use that ?

Clipping with an Asgard is highly unlikely. It also won't have any audible distortion unless it is defective.

OP

#### Karister

##### Member
Clipping with an Asgard is highly unlikely. It also won't have any audible distortion unless it is defective.
It has easily audible hiss when I connect Audioquest Nighthawk to it and nothing is played. RME is silent while Schiit produces hiss in headphones. It does not happen with FiFiMAN Arya. I guess Arya's low effectiveness kills this noise.

Regarding my sub bass test - Schiit is just one huge distortion when close to max volume in hi-gain. Bass sounds like videoconference with 1000 ping. I used all the same remaining gear with RME: same file, network player, headphones and cables. Schiit Bisrost 4490 Sigma-Delta + Asgard 2 just did not handle it. Replaced both with RME and sound was perfectly fine. I have used this song:
and this one:
. They are far from normal songs and it was definitely too loud for longer listening than a few seconds. RME somehow handles it while Schiit does not.

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