Ultrasonic difference tone hearing

Hi,

Is it true that you can hear a 2 kHz tone if you hear a 21 kHz tone + a
23 kHz tone? I've been arguing with someone about this. He says that
you can, but that goes against what I know about the effect in the
frequency domain of adding signals together in the time domain, not
only that but I tried playing a 19,560 Hz tone together with a 20,000
Hz tone through my PC speakers (which have a decent frequency response
in that range which I tested with a chirp and a mic) and I don't hear
any 440 Hz, unless I push the volume loud enough but in this case for
obvious reasons the actual signal contains low frequency components. It
also goes against my (erronerous?) conception of human hearing which is
pretty much to me a linear system just like a microphone or a loud
speaker.

So it makes me highly sceptical, however when I googled what he pointed
me to it seems that the reality of ultrasonic difference tone hearing
isn't even controversial, so I'd like to know, by what mechanisms could
we hear a 2 kHz tone from a 21 kHz tone added to a 23 kHz tone other
than through distortion, and if we can, why in my experiment did I fail
to hear a 440 Hz tone?

Thanks in advance

Michel Rouzic skrev:
> Hi,
>
> Is it true that you can hear a 2 kHz tone if you hear a 21 kHz tone + a
> 23 kHz tone? I've been arguing with someone about this. He says that
> you can, but that goes against what I know about the effect in the
> frequency domain of adding signals together in the time domain, not
> only that but I tried playing a 19,560 Hz tone together with a 20,000
> Hz tone through my PC speakers (which have a decent frequency response
> in that range which I tested with a chirp and a mic) and I don't hear
> any 440 Hz, unless I push the volume loud enough but in this case for
> obvious reasons the actual signal contains low frequency components. It
> also goes against my (erronerous?) conception of human hearing which is
> pretty much to me a linear system just like a microphone or a loud
> speaker.
>
> So it makes me highly sceptical, however when I googled what he pointed
> me to it seems that the reality of ultrasonic difference tone hearing
> isn't even controversial, so I'd like to know, by what mechanisms could
> we hear a 2 kHz tone from a 21 kHz tone added to a 23 kHz tone other
> than through distortion, and if we can, why in my experiment did I fail
> to hear a 440 Hz tone?

I know that certain sonar systems generate LF signals as the
difference between two HF source signals. The reason this works
is that the high-power source signals interact nonlinearly generating
strong components at the difference frequencies.

Assuming you are right that this is possible -- I have not heard
of such an effect before -- you ought to look for some nonlinear
interaction somewhere, between the HF source signals.

Rune

Michel Rouzic wrote:

> Hi,
> 
> Is it true that you can hear a 2 kHz tone if you hear a 21 kHz tone + a
> 23 kHz tone?

Yes. If the amplitudes are enough high.

> So it makes me highly sceptical, however when I googled what he pointed
> me to it seems that the reality of ultrasonic difference tone hearing
> isn't even controversial, so I'd like to know, by what mechanisms could
> we hear a 2 kHz tone from a 21 kHz tone added to a 23 kHz tone other
> than through distortion,

The air itself is the nonlinear media. The effects are very considerable 
when the sound levels are above 90dB.

  and if we can, why in my experiment did I fail
> to hear a 440 Hz tone?

The signal is not strong enough.

Vladimir Vassilevsky

DSP and Mixed Signal Design Consultant

http://www.abvolt.com

"Michel Rouzic" <Michel0528@yahoo.fr> wrote in 
news:1158843614.120699.126680@d34g2000cwd.googlegroups.com:

> Is it true that you can hear a 2 kHz tone if you hear a 21 kHz tone + a
> 23 kHz tone? I've been arguing with someone about this.

Well, 'hear' may or may not be accurate, the frequencies may not be right, 
and this has nothing to do with physics, but active function of the inner 
ear.

It turns out that hair cells can not only sense movement of the membrane in 
the inner ear, but they can actually tug on the membrane and cause the ear 
to actively emit sound that can be recorded by a microphone in the ear 
canal.  This is often used to test hearing systems, as it can be seen in 
healthy ears.  I'm not sure if the test subject actually "hears" the sound 
or not.

When you play two tones, the ear plays back other frequencies.  I think the 
most prominent is 2*f1 - f2, but there is also 2*f2-f1 and 3*f1-f2.  The 
2Khz number you cite seems to have left the factor of two off the f1.  The 
real answer would be 2*23-21= 25Kz, or maybe 2*21-23= 19kHz.  I can't 
remember whether f1 is the higher or lower freq. 

You can search up Distortion Product Otoacoustic Emissions for more info. 

-- 
Scott
Reverse name to reply

Scott Seidman wrote:

> "Michel Rouzic" <Michel0528@yahoo.fr> wrote in 
> news:1158843614.120699.126680@d34g2000cwd.googlegroups.com:
> 
> 
>>Is it true that you can hear a 2 kHz tone if you hear a 21 kHz tone + a
>>23 kHz tone? I've been arguing with someone about this.
> 
> 
> Well, 'hear' may or may not be accurate, the frequencies may not be right, 
> and this has nothing to do with physics, but active function of the inner 
> ear.
> 
> It turns out that hair cells can not only sense movement of the membrane in 
> the inner ear, but they can actually tug on the membrane and cause the ear 
> to actively emit sound that can be recorded by a microphone in the ear 
> canal.  This is often used to test hearing systems, as it can be seen in 
> healthy ears.  I'm not sure if the test subject actually "hears" the sound 
> or not.
> 
> When you play two tones, the ear plays back other frequencies.  I think the 
> most prominent is 2*f1 - f2, but there is also 2*f2-f1 and 3*f1-f2.  The 
> 2Khz number you cite seems to have left the factor of two off the f1.  The 
> real answer would be 2*23-21= 25Kz, or maybe 2*21-23= 19kHz.  I can't 
> remember whether f1 is the higher or lower freq. 
> 
> You can search up Distortion Product Otoacoustic Emissions for more info. 
> 

Yes, the 2*f1 = f2 is typically the strongest distortion product in 
EOAEs. For best results the f2/f1 ratio should be around 1.225.

Paul

> So it makes me highly sceptical, however when I googled what he pointed
> me to it seems that the reality of ultrasonic difference tone hearing
> isn't even controversial, so I'd like to know, by what mechanisms could
> we hear a 2 kHz tone from a 21 kHz tone added to a 23 kHz tone other
> than through distortion, and if we can, why in my experiment did I fail
> to hear a 440 Hz tone?
>
> Thanks in advance

Yes, there are  non-linearities that can casue "mixing products" in the
speaker, the air and in your ears...

Mark

Vladimir Vassilevsky wrote:
> Michel Rouzic wrote:
>
> > Hi,
> >
> > Is it true that you can hear a 2 kHz tone if you hear a 21 kHz tone + a
> > 23 kHz tone?
>
> Yes. If the amplitudes are enough high.
>
> > So it makes me highly sceptical, however when I googled what he pointed
> > me to it seems that the reality of ultrasonic difference tone hearing
> > isn't even controversial, so I'd like to know, by what mechanisms could
> > we hear a 2 kHz tone from a 21 kHz tone added to a 23 kHz tone other
> > than through distortion,
>
> The air itself is the nonlinear media. The effects are very considerable
> when the sound levels are above 90dB.
>
>   and if we can, why in my experiment did I fail
> > to hear a 440 Hz tone?
>
> The signal is not strong enough.

If I understand it correctly, this effects appear when the signal is
strong, so in a way, it's created by some kind of distortion, and from
the other posts in this topic, it has to do with how our ears are made
or the air itselves rather than something in our brain, right?

"Michel Rouzic" schrieb im Newsbeitrag > 
> Is it true that you can hear a 2 kHz tone if you hear a 21 kHz
> tone + a 23 kHz tone? I've been arguing with someone about 
> this. He says that you can, but that goes against what I know 
> about the effect in the frequency domain of adding signals 
> together in the time domain, 

google for "beat tone", e.g.
http://www.modrec.com/tutorials/beats.html

HTH
Martin

Martin Blume wrote:
> "Michel Rouzic" schrieb im Newsbeitrag > 
>> Is it true that you can hear a 2 kHz tone if you hear a 21 kHz
>> tone + a 23 kHz tone? I've been arguing with someone about 
>> this. He says that you can, but that goes against what I know 
>> about the effect in the frequency domain of adding signals 
>> together in the time domain, 
> 
> google for "beat tone", e.g.
> http://www.modrec.com/tutorials/beats.html

Martin,

Beat tones are not merely perceptual and needn't arise from any 
nonlinearity. Beat tones at frequencies below what is audible are 
readily perceived, as the examples you provided demonstrate. Plot the 
sum of the individual sinusoids and you will see why.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

Vladimir Vassilevsky wrote:
> Michel Rouzic wrote:
>
> > Hi,
> >
> > Is it true that you can hear a 2 kHz tone if you hear a 21 kHz tone + a
> > 23 kHz tone?
>
> Yes. If the amplitudes are enough high.
>
> > So it makes me highly sceptical, however when I googled what he pointed
> > me to it seems that the reality of ultrasonic difference tone hearing
> > isn't even controversial, so I'd like to know, by what mechanisms could
> > we hear a 2 kHz tone from a 21 kHz tone added to a 23 kHz tone other
> > than through distortion,
>
> The air itself is the nonlinear media. The effects are very considerable
> when the sound levels are above 90dB.
>
>   and if we can, why in my experiment did I fail
> > to hear a 440 Hz tone?
>
> The signal is not strong enough.

If I understand it correctly, this effects appear when the signal is
strong, so in a way, it's created by some kind of distortion, and from
the other posts in this topic, it has to do with how our ears are made
or the air itselves rather than something in our brain, right?

By the way, the context of this argument was a discussion on the
advantages of vinyl as opposed to audio CD, one argument in the favour
of vinyl being that it would record ultrasounds, thus allow those
ultrasonic difference tone to be heard, making it much better for the
audiophile.

I guess that's how audiophiles are supposed to explain the need for a
sampling frequency of 192 kHz.