Understanding How the Klippel NFS Works

[Sokel]

I am trying to understand what Linkwitz meant when he said that an ideal speaker is an acoustically small point source speaker. I can hear obvious differences between small speakers and large, and I am trying to understand that difference. I do not see any measurements that correlate with the difference that I can hear, hence the question.

I hear the same but coming to think of it,large speakers have greater distance between them (usually) and are placed in bigger rooms (again.usually) .
That's why I always consider speakers and room as a whole,big sound needs both.

 

[3ll3d00d]

acoustically small point source speaker.

It literally means it radiates as a monopole

 

[NTK]

Your other post also mentions comparing the real sound power vs. the apparent sound power. I had a look at the sections of the paper that you quoted, and the maths went a bit over my head. I take it that "real sound power" is what the Klippel actually measures, but I am not clear what "apparent sound power" means.

A little bit of math: Sound intensity (power of the sound wave per unit area, it is a local quantity that is location dependent) is the product of acoustic pressure and acoustic particle velocity (the oscillatory velocity amplitude of the air). Sound power is sound intensity integrated over a surface (usually spherical for simplicity, and the particle velocity is the velocity component normal to the surface) that fully encloses the sound source. It is the total acoustic power radiated by the sound source, and should be a constant independent of the integrating surface used when without air absorption.

Since there can be a phase difference between pressure and velocity, they are often expressed using complex numbers when we are dealing with sinusoidal (harmonic) waves. Therefore, the sound intensity is also a complex number. "Apparent" sound power refers to the magnitude of this complex number, whereas the "real" sound power refers to the real part of the complex number.

When pressure and velocity are in phase, as when they are in the far field, the product of the 2 quantities will be a real number (no imaginary part). For a real number, the magnitude and the (real parts of the) number are the same, therefore the "apparent" power and the "real" power are the same.

 

[Keith_W]

Thank you for being so patient. It took me several hours of googling and thinking to digest what you said. So let's see if I understand.

Firstly, I thought that pressure and velocity are always 180deg out of phase with each other - where pressure is maximum, velocity will be at zero. So I was a bit confused by your statement "when pressure and velocity are in phase". I mean, they can't be in phase? Maybe what you meant is that the phase relationship is constant? So: my interpretation of what you said is: in the nearfield, the phase relationship between pressure and velocity may be dependent on the position on the imaginary sphere where the observation was made, but in the farfield the phase relationship is constant. Would this be an accurate interpretation of your statement?

 

[NTK]

Thank you for being so patient. It took me several hours of googling and thinking to digest what you said. So let's see if I understand.

Firstly, I thought that pressure and velocity are always 180deg out of phase with each other - where pressure is maximum, velocity will be at zero. So I was a bit confused by your statement "when pressure and velocity are in phase". I mean, they can't be in phase? Maybe what you meant is that the phase relationship is constant? So: my interpretation of what you said is: in the nearfield, the phase relationship between pressure and velocity may be dependent on the position on the imaginary sphere where the observation was made, but in the farfield the phase relationship is constant. Would this be an accurate interpretation of your statement?

I had been thinking about a post on the math of how the near field to far field happens, basing on materials on standard acoustics textbooks. It will probably take me a few days. Hopefully I'll have something this weekend.

 

[Newman]

Thank you for being so patient. It took me several hours of googling and thinking to digest what you said. So let's see if I understand.

Firstly, I thought that pressure and velocity are always 180deg out of phase with each other - where pressure is maximum, velocity will be at zero.

Such a relationship would actually be 90 degrees out of phase, like sine and cosine.

So I was a bit confused by your statement "when pressure and velocity are in phase". I mean, they can't be in phase?

You might be thinking of displacement. Particle displacement is 90 degrees out of phase with wave pressure.

Particle velocity, however, is in phase with wave pressure.

Maybe what you meant is that the phase relationship is constant? So: my interpretation of what you said is: in the nearfield, the phase relationship between pressure and velocity may be dependent on the position on the imaginary sphere where the observation was made, but in the farfield the phase relationship is constant. Would this be an accurate interpretation of your statement?

I won’t get in the way of NTK’s interesting tutorial, just wanted to clarify that acoustic wave pressure and particle velocity are intrinsically in phase, as an acoustic pressure wave propagates through air.

 

[NTK]

I had been thinking about a post on the math of how the near field to far field happens, basing on materials on standard acoustics textbooks. It will probably take me a few days. Hopefully I'll have something this weekend.

I apologize. I've vastly over-estimated my productivity. Will need a few more days

 

[JimA84]

First of all is the measurement microphone. We could have a huge thread on microphone performance alone. None is perfect.

Then we have microphone placement.

And the number of microphones we use to capture the sound at a given moment at various positions.

Hardon Audio published a theoretical study about subwoofer placement with an infinite number of subwoofers.

You see the issue here.

Measuring sound with an imperfect microphone in an environment which may not reflect a home listening room is likely to lead to unrealistic expectations.

The only thing that really matters is the performance in the customer's listening room with the customer's equipment.

In addition to the customer's taste.

Even dedicated audiophiles sometimes find certain equipment flat or strident.

In my view we can eliminate really bad equipment but when you pass a certain point, it's probably best to offer the customer a variety of good solutions instead of one "best" option.

After all, one would hope that the enjoyment is ultimately about the music, not the speakers.

 

[Keith_W]

Hardon Audio published a theoretical study about subwoofer placement with an infinite number of subwoofers.

You see the issue here.

HAHAHAHAHAHA!!! "Hardon Audio!!!"

And you forgot the link. But you left enough hints for me to guess that it's Welti's classic multi-sub paper. Just a word of warning, Hardon Audio's paper is long, but the climax is worth persisting. You can read the presentation here. The Hardon publication is truly satisfying.

Ahem, I better stop before I get banned.

 

[amirm]

First of all is the measurement microphone. We could have a huge thread on microphone performance alone. None is perfect.

Good measurement mic is more perfect than a good speaker. So not an issue here.

As to rest of your comments, room is in control at lower frequencies. Above that, speaker is in control. So issue in the former, is not a reason to disregard the latter.

Also, your post is off-topic in this thread. Please continue elsewhere if you need to respond.

 

[René - Acculution.com]

As @NTK correctly states, in the far-field (assuming a propagating wave only, purely active), particle velocity and pressure are indeed in-phase. The confusion probably comes from thinking in terms of room modes, a purely reactive standing wave field without any propagation, where the two variables have a phase difference of 90 degrees. The impedance seen from the sound field dictates the phase relationship between these variables, and it does not have to fall directly into any special case.

 

[Keith_W]

As @NTK correctly states, in the far-field (assuming a propagating wave only, purely active), particle velocity and pressure are indeed in-phase.

To be honest, I am still confused by this. My understanding is that particle velocity and pressure are always 180deg out of phase - where particle velocity is highest, pressure is at zero and vice-versa. And also that this is an inescapable physical relationship. I am not arguing with you, I am sure that you and NTK are correct. I am only pointing out my own mental block. Your reply reminds me that I should go back and read Everest again, unless you know of a better resource?

 

[René - Acculution.com]

To be honest, I am still confused by this. My understanding is that particle velocity and pressure are always 180deg out of phase - where particle velocity is highest, pressure is at zero and vice-versa. And also that this is an inescapable physical relationship. I am not arguing with you, I am sure that you and NTK are correct. I am only pointing out my own mental block. Your reply reminds me that I should go back and read Everest again, unless you know of a better resource?

I think most sources on acoustics go into acoustic impedance, and specific acoustic impedance. Just as voltage and current are only in-phase in a resistor, but not in general as you add reactive components (inductors and capacitors), where there is an exchange between potential and kinetic energy between these components, phase will vary depending on where in the circuit you extract it. In an acoustic wave these reactive aspects come from the momentum (mass) and compressibility (spring) effects of the medium (air), but there might be standing and propagating waves in combination, and so there no particular requirement to the phase. There is only a requirement that for standard acoustics the particle velocity is proportional to the gradient of pressure, and that will hold in general.

 

[René - Acculution.com]

I just had a look at Everest (never heard of it before) and they explain phase very poorly (incorrectly), so go with Kinsler and Frey or something else where the signal processing is explained properly.

 

[Keith_W]

You mean the explanation of phase in this book is incorrect?

I just re-read section 1 on phase. It looks correct to me. What's wrong with it? If that book is wrong, then I have to question my own understanding of phase. BTW, you mentioned signal processing. It looks as if Kinsler and Frey is a book on acoustics.

 

[René - Acculution.com]

In Fig 1-10 they seemingly explain phase via time shifting signal, or time passing, it is unclear. That is the classical mistake of mixing up the phase coming from a delay, and then the actual phasor phase. If we stick to real numbers and real signals, not complex, a signal could be written as A*cos(wt+theta). If you call the whole argument in the cosine "phase", then yes, that will change as time passed. But that is not the phase that characterizes the signal, as that is theta only. Theta is the phasor phase, the relevant phase in the above discusssion. They also mention a "360 deg delay", so clearly they have this wrong way of thinking about phase, that I discuss in this article https://audioxpress.com/article/simulation-techniques-misconceptions-in-the-audio-industry. It is common both with hobbyist and engineers, and most Youtube videos on the topic are incorrect.

Also, in Fig 1-11 they talk about two signals of different frequencies being "in-phase". This is incorrect. Phase only makes sense on a 'per frequency' basis, not between different frequencies.

This is the problem with these "light-weight" books. You have to dig into the more complex aspects of signal processing before moving onto waves, as an example. Something like "Communication System" by Carlson has a very good introduction. I also have a long video on the topic of phase on the youtube channel Acculution.

 

[NTK]

This post is long overdue. I lost my motivation after reading and engaged in a bunch of bickering posts. My apology.

Quoting Eberhard Sengpiel (RIP): “Each sound source has a far field and a near field, which is only source dependent.” We can infer from Sengpiel's statement that the near field and far field characteristics, and how and where the transition takes place, are different for different types of sources.
(Source: https://sengpielaudio.com/DirectFieldAndReverberantField.pdf)

We'll start by looking at, AFAIK, probably the most elementary type of sound wave — a steady, single frequency sinusoidal plane wave. (Note: The purpose of the colors is to help keeping track of the air "particles". The color of each particle remains the same and is independent of its position.)

TL/DR — Plane Wave:

• In this discussion, a plane wave is an idealized pressure wave (in a uniform and stagnant medium) that propagates in a straight line in one direction. The pressure and other properties are uniform across any plane that is perpendicular to the direction of the wave propagation.
• It may be generated by an infinitely large flat wall with an oscillating motion. The plane wave propagates in the direction of the wall movement (and perpendicular to the wall).
• In a lossless medium — a reasonable assumption when dealing with distances typical for domestic listening rooms, the pressure of the plane wave does not vary with distance. The pressure at position r + δ is the same as the pressure at position r delayed by the amount of time it takes for the pressure wave to travel the distance of δ (delay τ = δ / c, where c is the speed of sound).
• Pressure and particle velocity are in-phase for a plane wave — pressure peaks and troughs are aligned to the velocity peaks and troughs. This alignment is typically a characteristic of being in the far field. There is no near-field / far-field transition for plane waves.

The More Elaborate Version:
The mathematical expression that describes the acoustic pressure field of this plane wave is shown below. This expression is a solution to the 1-D wave equation for pressure. (This solution shown is for a wave traveling to the right, i.e. in the positive r direction. A left-going wave is also a solution to the wave equation.)

Let's spend some time to examine this expression. In the second expression of p'(t, r), it can be seen that p'(t, r) is the product of 2 sinusoidal functions, with frequencies ω and k. When working with electrical signals, we often use the radial frequency ω = 2 π f = 2 π / T, where T is the period. Here we additionally have the acoustic wavenumber k, where k = ω / c = 2 π f / c = 2 π / λ, and λ is the wavelength. Comparing the two, k can be seen as the counterpart of ω, where ω is the radial frequency in the time domain, and k is the radial frequency in the spatial domain. At any given fixed time (constant t), p' gives a sinusoidal function in space. At any given fixed position (constant r), p' gives a sinusoidal function in time.

The relationship between pressure and “acoustic particle” velocity is given by the momentum balance equation, which basically is Newton's second law, F = m a. Plugging in the expression for the pressure and after a few mathematical operations, we have the expression for the particle velocity.

For the plane wave, the velocity at a given position is the pressure at the location divided by the product ρc, a quantity we call the characteristic impedance of the fluid. In electricity, from Ohm's law, we have: current = voltage / electrical impedance. The analog in acoustics is: velocity = pressure / acoustic impedance.

Since the characteristic impedance ρc is a scalar quantity (i.e. a real, not complex, number), and multiplication by a scalar has no impact on phase, pressure and velocity for plane waves are therefore in-phase.

The Standing Wave
Where pressure and velocity can get out-of-phase is in a standing wave. We have standing waves when we hit a room mode (resonance). As an example, we synthesize a standing wave by summing a plane wave and a copy of it but going in the opposite direction.

The particle velocity again can be calculated using the momentum balance. The mathematical manipulations of the last step of the derivation are not shown. Those unconvinced can take a look this from Wolfram Alpha (scroll down to the “Alternate forms”).

(-e^(i (omega t + k r)) + e^(i (omega t - k r))) / (e^(i (omega t + k r)) + e^(i (omega t - k r))) - Wolfram|Alpha

Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels.

www.wolframalpha.com

Particle velocity is pressure multiplied by a purely imaginary number, which means it is 90° out-of-phase with pressure for this standing wave.

 

[NTK]

Reserved for a post on spherical wave.

 

[NTK]

Reserved for a post on the sound wave generated by a rigid piston on an infinite baffle.

 

[René - Acculution.com]

(Source: https://sengpielaudio.com/DirectFieldAndReverberantField.pdf)

Be careful with Sengpielaudio; it is not all correct, for example the page on Phase has issues.

For the plane wave, the velocity at a given position is the pressure at the location divided by the product ρc, a quantity we call the characteristic impedance of the fluid. In electricity, from Ohm's law, we have: current = voltage / electrical impedance. The analog in acoustics is: velocity = pressure / acoustic impedance.

For acoustic impedance it is more accurate to say Volume velocity = Pressure/acou imp. For specific acoustic impedance it is as above.

Since the characteristic impedance ρc is a scalar quantity (i.e. a real, not complex, number), and multiplication by a scalar has no impact on phase, pressure and velocity for plane waves are therefore in-phase.

A scalar is generally complex, so multiplying a complex phasor with a real(!) scalar does not change the phase, but in general it does. The pressure field is a complex scalar field, whereas the velocity is a vector field. The complex value (phasor) related to the velocity should really be called the 'particle speed' as there also in an associated direction (as opposed to the pressure field), but nobody ever does that. We are 'lucky' in standard acoustics that we are dealing with potential fields, such that we only have to know the scalar pressure to then be able to know the velocity via a gradient, and other variables such as temperature and density are directly proportional to pressure. In microacoustics, for example, you will often have to calculate each one of these explicitly.