A question about the impedance and sensitivity of headphones

I'm really confused about my headphones' specs. My Grado GH4's impedance is 32 Ohms with 99.8db/mW sensitivity and my MM500 is 18 Ohms with 100db/mW. I tried in many equipments even with my iPhones, in the same volume displayed on the equipments, the GH4 is always much louder than my MM500, and RS1X I tried too is also louder than MM500 in the same way of GH4's with same specs of GH4. WTF. Is there some kind of higher theories in physics that I miss or have to know?

*Edit: wrongly write "mV" in a hurry on the post, but it should be mW.

 

Unrelated: Isn't your avatar from the MPD Psycho manga (note: MPD is no longer a valid diagnosis and the portrayal therein borders on supernatural, from memory)? Read that one ages ago, remember thinking it was really messed up and creepy, hah. Don't think I ever finished it, though.

Related: Do you mean louder in the sense that you get higher SPL readings measured at certain frequencies, or louder in the sense that you perceive it as louder? Not heard either the MM-500 or the GH4 specifically but looking at how they're voiced I can see how the more aggressive presentation of the GH4 might be perceived as louder.

While there's truth to higher impedance headphones being harder to drive, I don't think it's as simple as "higher resistance = lower volume", specifically, especially when you're comparing a dynamic headphone to a planar magnetic one as in here, since each transducer type has different requirements.

I'm not a particularly intelligent person so all I can offer is an overview, but it may help to hear what other specific amps you've tried pairing with them, since IME the general trend of higher-impedance headphones needing gobs more voltage than lower-impedance headphones (which need way more current) holds true.

For what it's worth, I certainly can get loud enough volumes on a Sennheiser HD600 (300R, 97dB/V or around 82dB/mW) out of an older phone like a Samsung Galaxy S9 or an Apple dongle, just that they sound really bland when compared to how they sound out of a less wimpy amplifier.

P.S.

This may be a better fit for the general purpose thread: https://superbestaudiofriends.org/index.php?threads/the-all-purpose-advice-thread-part-2.12149/

 

Yes, It's from MPD Psycho. I'm so surprised that this mange would be noticed in this forum, which in my country is spread in few people. I'm not a big fan about it, because I think the latter part of the story lacks of depth, but still cool to read if you're ok with tons of killing scenes.

Thank you so much for your reply. You mentioned measurements, and so I detect it (though in my phone) and the numbers make it all clear. Yes, actually MM500 is louder and I think Grado's aggressive and brightness make it be heard "louder". I'm sorry that I have make that stupid question without measuring it, cuz all my friends and I would turn it a bit down after hearing MM500 and switch into Grados.

 

Though I don't know if the professional detector would make a different number, because it's apparent louder.

 

Yes I think you are right. I just find Audeze says the min recommended power should be over 100mv and sensitivity is 100db/mv. What a joke!

 

Imagine that your amp has an output impedance of 18 Ohms. This creates a voltage divider with the headphones If you tried to drive 1V into the 18 Ohm phones, you would divide the voltage in half - 1/2V for the output impedance, 1/2V for the headphones. Into the 32 Ohm phones, the division would be closer to 1/3V for the output impedance and 2/3 for the phones. Thus your 32 Ohm headphones are getting ~30% more voltage, so they are louder.

 

Always seem to enjoy higher output impedance amps than ones that are closer to 0. Even with 80ohm focal elex 28ohms out of DNA Sonett2 is best I've ever heard them.

 

You are missing the correct sensitivity specifications. You have stated dB/mV but the mfg specs are dB/mW.
dB/milliWatt, not dB/milliVolt.

Additionally, those sensitivities are specified at 1 KHz only. Look at a given headphone's frequency response and align the 1 KHz point to the dB/mW spec. Now look at the deviation that occurs everywhere else on the spectrum. So it is possible to have a similar spec at 1 KHz but experience a significant difference in perceived sound levels.

The best way to match sound levels between headphones is using pink noise to headphones and a real time spectrum analyzer on mic from dummy head. That will result in a much better assessment of sensitivity. No one does it this way because it requires a lot more effort.

 

Oh, I'm sorry, actually it's dB/mW. I write it wrongly in a hurry.
*Have corrected it now.

Thank you for all these methods and knowledge. I will take it in mind.
Dummy head and analyzer with mic is too expansive for me, though I'm glad to analyze it if I have the equipments.

Oh I see, that's considerable and beyond my knowledge before. Thx!

 

I just did a quick google and found this calculator:
https://www.headphonesty.com/headphone-power-calculator/

 

Thx for your reply. I once tried it too, but I noticed it can't be accurate in amps, of which output impedance and equipment itself has many other specific things interfering it. And if my memory is correct, in different headphone impedance the output impedance and the watts on it would be different, which makes the calculator not that useful but still a thing to check. And I have looked into many descriptions that many amp would not have the specific output for 16ohms, but for 16 and 32ohms with a same and small output impedance. They share the same output impedance, so I think it might be in the same circumstance.

If I have the opportunity I would check it out with professional tools, I'm so curious about the truth.

 

When you turn the the volume knob of your amplifier, you are technically not controlling the power output, you are controlling the voltage output. The knob rarely controls the voltage in a linear fashion, typically it is logarithmic or a dual linear taper. Don't worry about this for now, but it's something to come back to later when you understand more.

Now in theory if your amp has a near-zero output impedance, and your headphone has a flat impedance curve (meaning it does not change over the frequency range), then the amp output voltage will go ~100% into your headphones across the entire frequency range and you calculate power as P = V*V/R where V is your output voltage and R is your headphone impedance (deliberately not using "I" because that looks like current).

So what does a headphone impedance curve look like? I grabbed this image from ASR. Note the horizontal scale which is frequency, and see how the impedance of the headphone changes a LOT, particularly in the midbass region around 100 Hz.


Now, look at the sensitivity spec provided by the manufacturer. That is a single number that is typically measured at 1kHz. It provides no info across the entire frequency range. Is your sensitivity higher or lower in the midbass? is it higher or lower in the treble?

Adding to the complexity, remember the formula for power is P = V*V/R, except now we see that R is low at 1kHz, super high at 100Hz, and has a bunch of wiggles at 2kHz, 4kHz, blah blah blah. Which means that our power calculation is all over the place depending on frequency. Add to that the fact we don't know the sensitivity at those frequencies.

Confused yet? Because we're not done yet.

Now add a non-zero amplifier output impedance into your equation. That statement I made above saying your amp voltage output goes entirely into the headphone is now no longer valid. I wish I could say that it was a simple fractional output over the entire frequency range, but in reality the output is going to be affected by the shape of the headphone impedance curve.

So now the voltage your headphone receives is a complex shape, the power calculated has that same complex shape applied again, the sensitivity number was only valid at a single frequency point, oh and let's not forget that music is actually a super complex combination of sounds encompassing the entire frequency range, and constantly changing.

With that all in mind now, let's go back to your original question:

Yes. Very much yes. Though not as crazy high as you may think.
The ability to calculate the power output based on any point of the curves should be something you can do with a high school physics background. With some basic measuring equipment you could even do a decent calculation to figure out sensitivity at different frequency points.

Calculating for actual musical sounds which are combinations of multiple frequencies at once is where it starts to get more complicated. Then there's stuff like distortion, THD, decay, and then there's the fun stuff with words like "Fourier transform" but that's above and beyond what most people should try to squeeze into their brains.

 

Now I understand. Thank you so much for your patience! Your words are clear and understandable and recall some of my college memories.Your informations are so straight to the point. I can't say more about how grateful I am. I'm sorry that I misread your opinion and for my naiveness. And I wish we can be friends to talk about so many things that interesting.

I know about the impedance curve and the voltage output. Analog signal is a voltage form if my memory is correct.[ And about the formula, P=V*V/R, in my country, it is taught in junior high school far from my age now, which I recalled and inferred from P=IV, and V=IR few days ago. However it still can't solve the problems without the specific datas, which makes me a bit frustrated.]Then I check many headphones how their curve look like but I can't measure it correct if I don't know about the curve of which different headphones could be completely different, And I know about different HZ must be different loudness and to me, I therefore want to know the average loudness, so there would be an easy way to measure, I think naively. Then I just thought about maybe it can make a bit sense with the specs manufactories give, and it confused me more.

And without the detector for these measurements, it's really hard to find out the truth of the headphones and manufactories' measurements are far from the truth, which leads to a myth that I think the calculator can't figure out well. And I'm glad that you can tell me and help me to recall these necessary informations.

 

Now I understand that that, beyond the basic basics, I never will understand!

Well... @Armaegis is truly a wonderful teacher: maybe I could learn from him. But I'd have to put in a lot of work, and numbers are among my least favourite thing. So, like with music... I tried to be a music student, and, in the end, settled for just listening.

Anyway, thanks to Armaegis for helping me scratch the surface.

 

Well, think about when you're forced to learn all these due to the examination-oriented education environment, it's really a bad taste to learn something you don't like. After I went to college, and I wanted to know more about how it works on the headphones, it starts make some senses and meanings, but I still can't say oh it's good for me to learn all these stuffs instead of chasing what I really love.

I maybe have said something really frustrating. Forget about it.

Cheer to you, my friend!