Where does the energy go?

[AtomicClock]

I'm no physicist, but my understanding of how a brass instrument works involves a standing wave inside the horn, and the low impedance at the bell allows sound energy to transfer into the room.

So what happens once you insert a practice mute? Is more energy reflected back into the standing wave? It certainly doesn't increase without bound. Do I subconsciously inject less energy into the mouthpiece? Is it absorbed by the soft tissue of the oral cavity? Does the horn get warmer?

[timothy42b]

I'm no physicist, but my understanding of how a brass instrument works involves a standing wave inside the horn, and the low impedance at the bell allows sound energy to transfer into the room.

With a wave in any medium, you get partial transmission and partial reflection at an impedance mismatch. The high impedance at the bell causes the reflection. Most of the energy is lost in the travel up and down the tubing. The acoustic books say 95% is lost. I don't know how that is calculated. I don't like the "standing wave" terminology because I don't think it helps understand this but it is commonly used.

So what happens once you insert a practice mute? Is more energy reflected back into the standing wave? It certainly doesn't increase without bound. Do I subconsciously inject less energy into the mouthpiece? Is it absorbed by the soft tissue of the oral cavity? Does the horn get warmer?

Resonance never causes increase without bound. You can find lots of diagrams with dotted lines as frequency approaches resonance, showing the amplitude going asymptotic to infinity. They are all wrong, and merely demonstrate bad math.

But your question about what happens to the energy is very insightful. I've never seen anyone wonder about that before. Kudos.

I don't know the answer. Probably someone else here does.

[hyperbolica]

My guess would be that the mute limits the wave such that it can only grow to a certain amplitude. This is after the bell is shaped in such a way to amplify the wave. To some extent, and with certain kinds of mutes, materials such as batting are used to dampen the wave.

To me, the standing wave is a great tool to help visualize what's going on at any given pitch within the air column.

The energy is coming from the mechanical energy of vibrating lips. Sound energy in general dissipates as a tiny amount of heating of the medium due to friction and reflection losses. But with a mute I would guess that the mute prevents some of the wave being amplified and/or some of the initial conversion from mechanical to pressure wave in the first place due to the back pressure.

[Doug Elliott]

I don't like the "standing wave" terminology because I don't think it helps understand this but it is commonly used.

The "standing wave" appears to be standing still but it's actually the result of a sound wave traveling down the air column and the reflection traveling back up the air column. It's the combined effect of two identical waves traveling in opposite directions.

[AtomicClock]

The acoustic books say 95% is lost.

This is interesting. I wouldn't have guessed that.

They are all wrong, and merely demonstrate bad math.

On par with frictionless systems and spherical cows.

[OneTon]

In an earlier post to a similar question, I said that what most people probably think is happening is not what is actually happening.

At low flows of air through the horn, some distance away from the mouthpiece and leadpipe, there is a mostly circular column of air flowing through the center of the horn. At low flows there can be a dead air space, or annulus, between the column of moving air, and the interior surface of the horn. If we put more air through the horn, the annulus is decreased or eliminated. The amplitude increases. We go from pianissimo to fortissimo. As we push more air through the horn, the volume increases and hopefully we stay on the same pitch, though at extremely soft or loud volumes the pitch will go slightly sharp or flat. Again, at low flows, the column may not be in contact with the surface of the horn. At higher flows, the column of air may be in contact with the surface of the horn as the internal pressure of the moving column of air is increased, or the width of the dead air annulus may be reduced.

The partial that we select is the frequency of the pitch. This pitch is riding on the column of air that we are blowing in to, or better yet through, the horn. If we increase the flow, by and large the pitch stays the same. Whether the flow is low or the flow is high, the vibration of the air column translates to the bell, causing the bell to vibrate, for the same reason that a similarly sized tuning fork rings when we strike an adjacent tuning fork with a rubber hammer,

We may have heard band directors tell their students to play softly, or more softly, but “blow the air through the horn.” The players blow through the horn, taking deeper fully breaths, instead of blowing at the horn. We saturate the column with support from our diaphragm. But we keep the diameter of the column of air the same. We may think that the analogy of the tuning fork becomes a little stressed at this point. However, we are not hitting the tuning fork any harder with the hammer. What we are doing is changing the time that head of the rubber hammer is in contact with the tuning fork. When the rubber hammer has more time to dwell on the surface of the tuning fork, the volume does not change but the intensity of the vibration does increase, which at small distances will be better translated to the adjacent tuning fork. Experienced carpenters, using obsolete, analog, handheld hammers, hit through a nail. Inexperienced carpenters hit at the nail instead of through it, and wear themselves out before the end of the day.

Now we stick the favorite mute of our choice in the end of the horn and are tempted to announce that, “all bets are off.” Let’s not get into too big of a hurry. The mute starts back flow resistance. As this happens, the flow is greatly reduced, Either the volume is reduced or we must “blow harder” to produce the same volume as the unmuted horn. The width of the dead air space of the annulus is decreased or eliminated, the intensity of the air column become more saturated, or the saturation intensity increases. This may vary along the length of the horn, or not. Depending on the flow, some parts of the horn may experience “signal” intensities that vary from other sections of the horn. Close to the mute, one set of partials are lit. Farther away from the mute, other partials may come into play. At softer volumes, some overtones become emphasized and others de-emphasized. At larger flows, some partials may override others. In any case, we may encounter a sound that is radically different from the unmuted horn. We don't change the length of the horn. The pitch may get squirrely, similar to going sharp at soft dynamics, but we stay in the same ballpark. On the other hand, the goal of a hotel mute is to provide a similar resistance to an unmuted horn, at a softer dynamic, without loss of consistent intonation and perhaps increased distortion, evenly across the range of the instrument. The player or designer of mutes may feel like electrical engineers, largely trained in a digital world, trying to adapt to or design an analog rf antenna.

Jay Friedman, Steve Turre, and Gordon Wycliffe are athletes, as well as the late Terry Clark. They developed strong diaphragms and expanded lung capacities, and selected mouthpieces, leadpipes, and trombones that produce sounds that are consistent with the genre that they are playing. Regardless of the equipment that is chosen, air control is king. This may be why Clark Terry was known to say, "It ain't the horn."

[timothy42b]

In an earlier post to a similar question, I said that what most people probably think is happening is not what is actually happening.

At low flows of air through the horn, some distance away from the mouthpiece and leadpipe, there is a mostly circular column of air flowing through the center of the horn. At low flows there can be a dead air space, or annulus, between the column of moving air, and the interior surface of the horn. If we put more air through the horn, the annulus is decreased or eliminated.

Interesting. I would not expect that. The boundary layer of course does not move, but I would have thought there was a continuous velocity gradient from boundary layer out.

However, air flow is not sound flow. The velocity of air flow is a small fraction of the velocity of the sound wave, and in fact the sound wave can travel fine if the velocity of air flow is zero. So I don't see any reason that the sound wave would not extend completely side to side in the walls of tubing (until the impedance change in the bell flare of course.)

[BGuttman]

Remember, air flow is essentially inviscid. There probably is a boundary layer but it is so thin as to be negligible.

Sound waves are actually air motion. They are compression waves as opposed to the sinusoidal waves we associate with electronics and optics.

A practice mute collects the sound waves in a "dead zone" drastically attenuating them. There isn't much energy in the waves so you probably won't be able to sense the heat buildup as the energy is dissipated.

[jorymil]

The short answer: heat!

That's of course a glib answer, but it's true for pretty much every system in nature (in this case, longitudinal pressure waves in air). The energy in the air column is absorbed by the mute, the walls of the instrument, and the player's body. You'd have to set up some experiments to measure how much: I'd be interested to see IR images of a trombone being played, for example. And you could put a couple of temperature sensors into a practice mute pretty easily (think Silent Brass, but with temperature sensors added). There are artificial embouchures that have been developed, and you could use those to measure input energy.

For what little it's worth, I do have a bachelor's in physics, but brass instruments are not exactly covered in extensive detail in the curriculum! I generally reach for _The Science of Brass Instruments_ or _The Physics of Musical Instruments_ .

[AtomicClock]

The short answer: heat!

This is what I would have said at the outset had I known about timothy42b's 95%. If it's that easy for the energy to migrate over to the brass tube, then another few percent would hardy be noticeable.

_The Physics of Musical Instruments_

I can get this one through interlibrary loan. I'll have a look.

[ghmerrill]

But your question about what happens to the energy is very insightful. I've never seen anyone wonder about that before.

It reminds me of the introductory tour of our physics lab when I was a freshman, and was done prior to the start of classes. One of the grad students was demonstrating how an oscilloscope worked and talking about electrons hitting the screen and losing energy. One of the wise-ass freshman asked "So where do the electrons go after they hit the screen? Do they just fall down to the bottom and then build up?" That stopped the grad student in his tracks for a few moments, but he did ultimately recover from it in a more or less sane way.

I have always viewed acoustics as something that seemed as though it should be pretty simple, but is in fact hideously complicated.

[jorymil]

As I said, very glib answer on my part, since pretty much _all_ energy loss in _any_ system goes to heat. The interesting bits are in where that energy gets absorbed. Could be in the walls of the instrument, the cork/rubber of the mute, or the walls of the mute. The energy could also just stay in the pressure wave of the air column, being reflected perfectly by the mute, but likely not. I'd be curious to see what the Yamaha engineers have learned: I don't know that there's much competitive advantage in the old mute system, for example.

As for the electrons hitting the screen, it's a fair question, and I'd hate to be put on the spot like that! As a teacher, "I don't know" is an answer that requires a lot of courage.

[ghmerrill]

As for the electrons hitting the screen, it's a fair question, and I'd hate to be put on the spot like that! As a teacher, "I don't know" is an answer that requires a lot of courage.

Looking back over the years, I've thought that the grad student really did know the answer but was temporarily stymied by trying to produce an explanation to a group of students who weren't conversant in quantum theory.

[OneTon]

The first law of thermodynamics say you can’t win. The second law says you can’t break even. And the third law saya you can’t get there from here. So “It’s heat”
Is always true. As part of the signal generator, the open horn is an inefficient reflector and the insertion of a mute introduces a more efficient reflector. “Ambient” heat, from playing outside or our breath, and/or full or very loud dynamics make the horn go flat with an open bell. Ambient lack of heat, or cold, and extreme dynamics at pianisimo make the pitch go sharp, as in attempting to play outside on a cold and windy day, or a dark and stormy night. In any of these cases the ambient condition is not quite steady state. Hence, the pitch fight’s on.

Hot or fast air has more energy , pushing the implied length of the open bell out. Air lacking heat or slow air will cause the implied length of the open bell horn to shorten, increasing the pitch, because the standing wave is shorter due to the lower energies failing to push that spongy, imaginary trampoline as far.

The inserted mute chokes the flow of air increasing the time that heat can be transferred. The butt of the mute may act as a hard reflector in and of itself, or we may get that imaginary moving trampoline effect, albeit altered from the open horn. Attributes of good mutes may include less of a pitch change when inserted, less pitch change at varying dynamics, and less pitch change over the range spectrum of the player. The mute also affects the flow rate of air, and can cause the pitch to drift up or down at increased or decreased dynamic inputs, depending on the design.

The actual dimension of the dead air boundary layer could be thick or thin, and difficult to measure. Classical Newtonian physics is most probably sufficient for this analysis: Quantum effects can be ignored, and Schrödinger’s cat will live another day.

[jorymil]

As for the electrons hitting the screen, it's a fair question, and I'd hate to be put on the spot like that! As a teacher, "I don't know" is an answer that requires a lot of courage.

Looking back over the years, I've thought that the grad student really did know the answer but was temporarily stymied by trying to produce an explanation to a group of students who weren't conversant in quantum theory.

I thought about it some more this afternoon. Thermionic emission of electrons, followed by a small acceleration/deflection tube (the actual TV tube), colliding with a phosphorescent screen, then presumably being attracted to a positive ground terminal of some sort, though there might be some residual electron gas as well? I'd definitely have to look it up.

[peteedwards]

“Ambient” heat, from playing outside or our breath, and/or full or very loud dynamics make the horn go flat with an open bell. Ambient lack of heat, or cold, and extreme dynamics at pianisimo make the pitch go sharp

This is exactly backwards. Sound waves travel faster in hot air, making the pitch rise, about 1-3 cents per degree Centigrade.

https://acoustics.org/pressroom/httpdoc ... rland.html

[jorymil]

The mute also affects the flow rate of air, and can cause the pitch to drift up or down at increased or decreased dynamic inputs, depending on the design.

Are you sure there's a meaningful flow of air? We often talk about airflow as trombonists, but this isn't the way sound waves work: air vibrates back and forth, but the net velocity of the air is quite slow. For example, perfume sprayed in front of a loudspeaker still takes the same amount of time to diffuse throughout a crowded room--possibly not for a song or two. Similarly, when an emergency siren goes off, you hear the noise as quickly as sound travels, but the air molecules of the ambulance never reach you: it'd require a _very_ fast wind to make that happen.

There's definitely a small flow of air coming out of the mouth, but its volume is way, way smaller than the volume of the air column. Instead, my understanding is that the air coming from the mouth serves to maintain and change the characteristics of the air column. Experiments have been done where the mouthpiece opening is actually sealed off with a membrane: the trombone still sounds the same! Or by buzzing a mouthpiece into a balloon, or at a longer length, using the bell covers often used during COVID. The idea of airflow is a useful _mental_ model for how to manipulate the lungs and oral cavity, but we do not blow _through_ the horn in a meaningful way, and there is little to no net velocity of the air inside the horn--it's all vibrational in nature.

Section 2.1.5 in _The Science of Brass Instruments_ goes into this a bit more--definitely worth a read for those who are interested.

As for quantum mechanics, yeah... it would greatly surprise me if there were quantum effects involved in trombone playing... but it would be cool!

[OneTon]

Get out the popcorn, Harrison.

The mute also affects the flow rate of air, and can cause the pitch to drift up or down at increased or decreased dynamic inputs, depending on the design.

There's definitely a small flow of air coming out of the mouth, but its volume is way, way smaller than the volume of the air column. Instead, my understanding is that the air coming from the mouth serves to maintain and change the characteristics of the air column. The idea of airflow is a useful _mental_ model for how to manipulate the lungs and oral cavity, but we do not blow _through_ the horn in a meaningful way, and there is little to no net velocity of the air inside the horn--it's all vibrational in nature.

"Way smaller" is not zero. If it were zero, then there would be no need to ever learn how to circular breathe.
Brass players would not "run out of air" when maniac directors held the last note of a composition for long periods of time. The model of a moving medium, such as a shallow river or stream, better fits what qualitatively happens with a trombone. The standing wave is generated when the current encounters a perturbation. Standing waves are generated in the river or stream against the direction of flow. It is true that the standing waves do not move up or down away from the obstacle. They are "standing." If the medium of the current ceases to flow, the standing waves collapse. If we quit blowing, the sound stops. If we only quit vibrating our lips, the sound stops. But the standing wave continues to exist if the air is flowing. When the flowing air arrives at the end of the bell, the momentum of the flowing air sees the ensued disorganization as a spongy, inefficient wall, which reflects a wave back upstream in the horn, perhaps a 1/4 wavelength out of phase, with no significant loss of heat, similar to reactance in an electrical circuit. Do we sustain the same tone when the mouthpiece is inserted in the horn longer than we sustain a tone generated by buzzing a mouthpiece?

Are you sure there's a meaningful flow of air? We often talk about airflow as trombonists, but this isn't the way sound waves work: air vibrates back and forth, but the net velocity of the air is quite slow. For example, perfume sprayed in front of a loudspeaker still takes the same amount of time to diffuse throughout a crowded room--possibly not for a song or two. Similarly, when an emergency siren goes off, you hear the noise as quickly as sound travels, but the air molecules of the ambulance never reach you: it'd require a _very_ fast wind to make that happen.

This is apples and oranges. Loudspeakers and sirens are more like dropping a pebble in a stagnant pond. At very close distances the air off a loudspeaker driven by a bass amp might be felt by a hand. It might even blow out a lit match's flame. Likewise, the height of waves generated by the pebble might reach a hand in close proximity to the previously stagnant surface. There is no net flow for loudspeakers and sirens. The molecules in the vicinity of the end of the open trombone bell are not likely to ever reach someone sitting 12 feet across a room full of still air, either. What happens in a trombone is better represented by the standing wave generated by a moving medium because Mother Nature gets angry when we don't conserve energy. She gets really angry when we blow into one end of the trombone and can't account for what happened to the initial flow of air.

The favorite trick of a professor with a PhD in petroleum engineering was to light a cigarette in the classroom. Incidentally, he loved to smoke. He then would state that the column of air produced by the rising smoke was "laminar" until it turned into "turbulence" represented by the swirling disorganized cigarette smoke. The cigarette stank. The analogy had a distinct odor as well. The Reynolds number of the disorganized flow was far too low to be called turbulent as it is typically defined. Relentless friction took its toll on the circular motion of the swirling smoke, which was less than the vertical column of organized flow, and soon stopped it altogether. However, the organized flow of the cooled rising cigarette smoke that then transitions into a stagnant disorganized swirl may be a visual picture of what is happening at the end of our bells. The stopped disorganized flow looks like a "wall." And it is also why at low flows, the organized flow of air may be buoyed by an annular cushion of stagnant air in proximity to the surface inside the horn.

The model of the referenced book as stated may suffice or even represent well the physics for a given calculation. If it does great. The moving medium model better fits what is actually happening in a trombone.

[2bobone]

"Paralysis by analysis". {Arnold Jacobs]

[AtomicClock]

"Paralysis by analysis". {Arnold Jacobs]

Totally inappropriate. There is no paralysis going on here. And I fear you mean to imply that all analysis is dangerous. What a dangerous attitude.

[atopper333]

"Paralysis by analysis". {Arnold Jacobs]

“if you have nothing nice to say, say nothing at all.” -Charles Caleb Colton

[2bobone]

"Totally inappropriate. There is no paralysis going on here. And I fear you mean to imply that all analysis is dangerous. What a dangerous attitude."

“if you have nothing nice to say, say nothing at all.” -Charles Caleb Colton"

WOW !! Did I step in that !! After I clean off my shoes I'll politely remind everyone that this a forum where thoughts on all matters are supposed to be considered, discarded or accepted ---- nothing more. I implied nothing nefarious and apparently Arnold Jacob's words of wisdom have become meaningless at this point. Now, back to the previously scheduled programming. Count me out.

[atopper333]

After I clean off my shoes I'll politely remind everyone that this a forum where thoughts on all matters are supposed to be considered, discarded or accepted

I couldn’t agree more. You are very correct. That is exactly what this forum is for. This particular thread is very theory heavy, and it was started that way on purpose. It is meant to ask an interesting theoretical question. The topic in and of itself is meant to provoke analysis. Comments concerning this to be paralysis are unproductive in a discussion based on…analysis and theory.

By all means, I do not argue the wisdom of your original quote, but like all things, there is a time and a place, and whether unintentional or not, its place here serves to narrow the discussion on this topic which doesn’t contribute to the open mindedness of the forum…

No ill will meant on my behalf…just questioning how appropriate that quote is in this thread…

[OneTon]

Count me out.

"Paralysis by analysis". {Arnold Jacobs]

Let's chill out. I appreciate the intent to keep negativity out of this forum. I think Arnold Jacobs" quote is kind of funny. 2bobone did not intend malice. It is a quote by Mr. Jacobs. Jorymil's model may work better where a calculation is desired and provide better understanding for some folks. My model may have a little more traction where acoustics are behaving more like RF in electrical engineering, and be clearer to other folks. I don't think anyone is going to change how they play based on either of these models. If it does, please post it here or send me a pm or email.

Peace,

[Cmillar]

I think that 'theory' meets 'reality' in our most important brass players' exercise: the crescendo/diminuendo

pp<ff>pp

(Fred Fox, the late great french horn guru, goes into the importance of this exercise in great detail in his wonderful book "Essential of Brass Playing".)

It's probably the most 'boring' exercise to actually remember to do, and I'm guilty of having neglected it more often than remembering to actually do it over the years.

But, it definitely seems to be THE exercise that deals with the 'horn/standing wave - human interaction' balancing act.

I've gotten back into this exercise (but doing the Doug Elliott-version) again on a regular basis, as I've been playing more music on my large bore horn recently and have needed to regain 'the sound'. It's done wonders for getting 'back into' the 88H when needed, and the carry over effect to the small horn is amazing.

It's like my new 'Zen' for trombone. Just doing this exercise puts everything else into it's proper perspective... and, making music is easier and more fun.

(Now, the challenge is to get a student to realize how important this 'boring exercise' is!)

[timothy42b]

The mute also affects the flow rate of air, and can cause the pitch to drift up or down at increased or decreased dynamic inputs, depending on the design.

Are you sure there's a meaningful flow of air? We often talk about airflow as trombonists, but this isn't the way sound waves work: air vibrates back and forth, but the net velocity of the air is quite slow.

A pressure impulse travels up and down the horn. The air flow is only necessary to make the lips buzz.

Similarly, electrons in a wire move more slowly than you walk, a few millimetres per second. Yet electricity flows near the speed of light. (well, actually exactly at the speed of light in copper, but somewhat slower than the speed of light in vacuo).

[BGuttman]

The thing about electrons is that the electron you put into one end of the wire is not the one that exits the end. Current flows due to a sequence of electrons jumping from atom to atom. Probably not that different from how the compression wave moves through the air column.

[harrisonreed]

If only electricity could flow faster then causality. We would be able to ask Arthur Pryor his thoughts on the subject.

[baileyman]

...
A pressure impulse travels up and down the horn. The air flow is only necessary to make the lips buzz.

...

Bob Sanders writes in confirmation:

https://bobsanders.net/airflow-through- ... ument.html

but click through to the video demonstrating zero air flow:



at about 2:31

[AtomicClock]

It's too bad that interesting video has such awful muzak.