Sound question

[MigL]

Totally agree with you Studiot.

The ear is sensitive to phase difference so we have two for comparison purposes, cetainly not to absolute phase. How could it be since an ear is the equivalent of an inverse speaker, i.e. a drum which converts translation/vibration to bioelectric signals ?

And as you say the speaker experiment demonstrates this very well.

[studiot]

Here are some results.

I offer them initially without comment other than they are obviously different.

 

 

 

 

[davidivad]

not to sound too stupid here studiot, but could this have anything to do with Helmholtz resonation?

if you put a tube into a speaker box at the location, then you cause constructive interference.

since the sound only has one hole then this would be more complicated.

in other words there are natural areas that will have destructive interference too.

in the end, there will be a predictable dead spot in the center of the tube. this is where the sound waves cancel out. of course you should also hear the phase velocity which is reminiscent of listening to the uneven operation of a fan. i would call this the "wowowowwoow" of the ring. it may be too slow or fast to hear though.

i hope i did not just waste your time.

i still think you should check out the toilet's "ring."

[Acme]

Your graphics department definitely produces prettier work than mine.

Do they work for free?

 

Yes they work for free, but they only work on what they want to.

 

Your ears are not reliable equipment for detailed investigation of the phenomenon.

What did you say?

 

Even function, who is much younger than I am, and deserves all the credit for noticing this, does not have good enough ears.

But remember, it is the sound in the air we hear, not the vibrations in the bell.

Here is the key phrase, extracted from your reference, which exactly mirrors my suprise finding.

 

acoustics link in post #74

The fundamental frequencies of the internal acoustic field are not well matched with the natural frequencies of the bell, which is different with what most of the researchers expected.

The diagrams from your link are similar to those from my post#14 and the comment noted above is exactly what I said about my diagram c in post#14.

 

studiot post#14

So there is significant acoustic impedence mismatch between the systems.

I did not fully pursue the implications of that at that time but it is the underlying mechanics of the effect.

 

Roger. I think I may be getting it. So colloquially speaking, there is not enough space inside the bell for the sound to 'develop'. ??

[studiot]

 

i still think you should check out the toilet's "ring."

 

 

My ears are too old to catch the high frequencies involved.

 

 

A helmholtz resonator requires a nearly enclosed chamber of air coupled to the source by a narrow constriction.

The plug of air in the constriction bounces up and down on the air in thachamber and, if the dimensions are correct, extracts energy from the outside air, transferring it and trapping it within the chamber where is is dissipated as heat.

That is how a car exhaust 'silencer' works.

The energy is transferred from the air to the walls of the chamber.

 

My bell is the opposite (has no cosntriction) , it transfers energy from the walls of the chamber to the air, flaring out like a horn.

The flaring does not assist the transfer of energy directly (the walls of a horn do not intentionally vibrate) it assists the spread of that energy.

 

I keep repeating that I have looked for nodes and antinodes in the sound, but not yet found any.

Edited April 12, 2014 by studiot

[davidivad]

i would say that it IS constricted because there is no port.

[studiot]

 

for the sound to 'develop'

 

Just the lower frequencies.

 

Compare the two spectrograms.

 

Ouside the bell there is significant response in the lower frequencies (hundreds of Hz)

 

Inside the bell the response is skewed towards the higher frequencies (thousands of Hz)

davidivad

i would say that it IS constricted because there is no port.

 

 

Perhaps you could engage Acme's graphics department?

 

A sketch or three is worth .............

 

Edited April 12, 2014 by studiot

[Acme]

 

...for the sound to 'develop' ...

Just the lower frequencies.

 

Compare the two spectrograms.

 

Ouside the bell there is significant response in the lower frequencies (hundreds of Hz)

 

Inside the bell the response is skewed towards the higher frequencies (thousands of Hz)

 

Roger. And that difference is because the lower frequencies have longer wavelengths that don't fit inside, whereas the higher frequencies have shorter wavelengths that do fit. Oui? By jove; I think I've got it!

[Enthalpy]

[...]

Edit: So I found a stainless pot lid about 8" across to experiment with. Definitely louder outside near the rim than inside at the plane of the rim. But sticking my ear further inside the loudness did increase as I was suggesting earlier. So is 'loudness' not the right term for what we're investigating?

I also rotated the lid as it was ringing and with my ear on the outside near the rim the loudness seemed to go up & down. Is that because of the nodes & antinodes?

 

You're getting forward, congrats in this misleading context.

 

If you have a flexible narrow tube and put one end in your ear, you can explore deeper in the bell and observe that the sound is weaker at the rim. Or use a small microphone.

 

Yes, you have heard the nodes and antinodes, because a bell has a multipolar pattern, instead of being an isotropic source. The first mode is a quadripole, consistent with the animated picture.

 

Maybe this discussion reaches flexural waves some day, who knows. Because, well, a compression wave at 6,000m/s would let a 0.1m diameter bell resonate at 20kHz which wouldn't be audible.

 

By the way, an acoustic resonance does not need a resonator bigger than half a wavelength. A Helmholtz resonator, like a glass bottle, is much smaller.

 

The two modes on the animated picture you linked correspond to nearly-degenerated modes. The first pair of modes of a bell are quadripolar, they look the same but are 45° apart from an other. If the bell has no perfect cylindrical symmetry, then these two modes have different frequencies and produce a beat, which sounds badly: it's a "broken bell".

 

I believe that higher pairs of modes are always detuned in a bell, and that this is a condition to sound like a bell.

[studiot]

 

So I found a stainless pot lid about 8" across to experiment with

 

Good on you for experimenting.

 

My bowl has a turned over lip that considerably stiffens the rim and changes the modes of vibration compared with a plain edge.

 

Many pan lids are the same, how is yours?

 

Further, ask yourself why does a tuning fork have two prongs yet is considered a single point sound source?

 

 

Enthalpy

 

1) I believe that higher pairs of modes are always detuned in a bell, and that this is a condition to sound like a bell.

 

2)

Maybe this discussion reaches flexural waves some day, who knows. Because, well, a compression wave at 6,000m/s would let a 0.1m diameter bell resonate at 20kHz which wouldn't be audible.

 

1) I'm always happy to discuss real physics, so how does this fit with the spectrum analyser results I posted?

 

2) The edge stiffening makes longitudinal flexion more likely. However did you follow up the Penn State University research results I posted?

 

They shows that flexural waves are replaced by shear waves at higher frequencies, amongst other things.

 

They used ordinary steel which has a compression speed of 5000 m/s. All the figures I could find for stainless average some 20% higher. Some are obviously above this average and some below. That is how I came by the figure of 6000 m/s.

[Acme]

Good on you for experimenting.

 

My bowl has a turned over lip that considerably stiffens the rim and changes the modes of vibration compared with a plain edge.

 

Many pan lids are the same, how is yours?

Danke. Mine has a shaped rim; see attached photo.

 

Further, ask yourself why does a tuning fork have two prongs yet is considered a single point sound source?

I asked and myself is thinking about it. He can be so dense sometimes.

[Acme]

snip...

Further, ask yourself [Acme] why does a tuning fork have two prongs yet is considered a single point sound source?

snap...

Ok. Myself answers because it acts just like a bell and we don't call 'a bell' 'bells' just because we can rotate it. Choose a plane through a bell's axis of rotation and you could chop a tuning fork out of it.

[studiot]

 

Acme

Choose a plane through a bell's axis of rotation and you could chop a tuning fork out of it.

 

 

Not quite since the free end of a tuning fork is not edge stiffened, however function's chalice may not be and so the analogy would be apt.

 

Whatever, the following animations are interesting.

Scroll down to the end of the apge and click on the frequency for the tuning fork animations.

 

http://www.ibp.fraunhofer.de/en/Expertise/Acoustics/Fundamentals-and-Software.html

 

But I keep saying this mantra.

 

What we hear is the sound in the air not the vibrations of the oscillator.

 

The air is being driven by the oscillator. The oscillator provided a forcing function.

 

When the air is unconfined as in a large space such as a room, or better a field, then there are no resonance effects the wave just spreads out.

The air has no preferential frequencies so the sound follows the oscillator.

 

When the oscillator is driving a body of air as a whole in a confined space (such as inside the bell, loudspeaker cabinet, helmhotz resonator or whatever), the physics is different since the oscillator is now exciting vibration modes of the air as an object. One difference is the measurable difference in frequency spectrum of the sound.

The inside air, acting a a body, now transfers energy to its preferential parts of the spectrum, as with any forcing function to a resonant system.

The transfer to higher frequencies is entirely consistent with the analysis performed earlier. This is a resonance/forcing phenomenon, not an interference one.

Energy calculations are difficult via vibration analysis and best done via adiabatic air theory. This sidesteps the inherent non linearity due to gamma being about 1.4 for air.

Our (my) ears are not particularly sensitive to this, particularly as I am hearing the outside sound(which I know is louder) in one ear and the inside sound in the other. So my brain is tricked into thinking they are the same. A typical masking phenomenon.

Edited April 15, 2014 by studiot

[Enthalpy]

Further, ask yourself why does a tuning fork have two prongs yet is considered a single point sound source?

 

If a tuning fork is alone in air, it's a bipolar souce.

Though, its bottom is commonly put on a wood part that radiates more strongly for being bigger - and sometimes at a resonator. The bottom (middle of the U shape) vibrates with a small displaceent that fits the wood part better. This movement can result in a monopole source if a resonator is used, often a quarterwave box.

2) The edge stiffening makes longitudinal flexion more likely. However did you follow up the Penn State University research results I posted?

 

They shows that flexural waves are replaced by shear waves at higher frequencies, amongst other things.

 

They used ordinary steel which has a compression speed of 5000 m/s. All the figures I could find for stainless average some 20% higher. Some are obviously above this average and some below. That is how I came by the figure of 6000 m/s.

 

It is perfectly known that flexural waves become shear waves at higher frequencies, at about the frequency where both propagation speeds get equal. You almost got away from compression waves, go on, that's the right direction.

 

Sound is slower in usual austenitic stainless steel, and by less than 20%. Wrong figures somehow. 6000m/s would be very much. Anyway, compression waves are irrelevant in a bell.

 

5000m/s would give a resonance outside ear's range, so it's about time to change your opinion. No compression wave.

Energy calculations are difficult via vibration analysis and best done via adiabatic air theory. This sidesteps the inherent non linearity due to gamma being about 1.4 for air.

 

At very high pressure swing, acoustics get nonlinear because P*V is a product. It stays nonlinear whatever the gamma.

Anyway, sound is linear at the sound pressure levels produced by a bell.

 

Nonlinearities are observed at pressure swings near one atm, which is the case in brass instruments. Musicians can blow air with 0.3atm overpressure in the lungs (3m water depth). The first research paper investigated a trombone and wanted to explain that way why the sound gets harder at fortissimo. They did see the nonlinear propagation of a strong pressure front, similar to an explosion pressure front.

 

Though, whether this causes the harder sound, or rather the hard beat of the lips at fortissimo, is discussed.

[studiot]

 

studiot, on 15 Apr 2014 - 7:40 PM, said:

Energy calculations are difficult via vibration analysis and best done via adiabatic air theory. This sidesteps the inherent non linearity due to gamma being about 1.4 for air.

 

 

Enthalpy post#89

At very high pressure swing, acoustics get nonlinear because P*V is a product. It stays nonlinear whatever the gamma.

Anyway, sound is linear at the sound pressure levels produced by a bell.

 

Using the product P*V is incorrect, although even Newton made this error. That is a pity since there is inverse proportionality ie if you double the pressure you halve the volume and so on. In this sense the P*V relationship is linear. The ratio is independent of the starting values and is constant.

 

Using the correct adiabatic expression does not enjoy this cosy relationship of ratio, it depends upon the actual values.

 

 

 

studiot, on 14 Apr 2014 - 8:30 PM, said:

2) The edge stiffening makes longitudinal flexion more likely. However did you follow up the Penn State University research results I posted?

 

They shows that flexural waves are replaced by shear waves at higher frequencies, amongst other things.

 

They used ordinary steel which has a compression speed of 5000 m/s. All the figures I could find for stainless average some 20% higher. Some are obviously above this average and some below. That is how I came by the figure of 6000 m/s.

 

Enthalpy post#89

 

It is perfectly known that flexural waves become shear waves at higher frequencies, at about the frequency where both propagation speeds get equal. You almost got away from compression waves, go on, that's the right direction.

 

Sound is slower in usual austenitic stainless steel, and by less than 20%. Wrong figures somehow. 6000m/s would be very much. Anyway, compression waves are irrelevant in a bell.

 

5000m/s would give a resonance outside ear's range, so it's about time to change your opinion. No compression wave.

 

 

Extract from Kaye & Laby, for speeds of sound in solids all in m/s

 

Mild steel

Longitudinal bulk waves 5960

Waves in thin sections 5196

Shear waves 3235

Rayleigh Waves 2996

 

Stainless Steel

Longitudinal bulk waves 5980

Waves in thin sections 5282

Shear waves 3297

Rayleigh Waves 3045

 

Penn University rated its sample as mild steel with a velocity of 5000m/s

 

I keep repeating this, the action of the bell is a (complicated) vibration, not a wave.

But you do not hear this action.

You only hear the sound in the driven air.

 

As to the frequency in the air, I was suprised that so many higher frequencies were present, but measuement shows that they are, and not all harmonically related.

This implies that the mode of vibration of the bell is acting in 'panels', with small panels of bell wall producing the higher frequencies. This is consistent with the images in the articles I linked to.

 

 

studiot, on 14 Apr 2014 - 8:30 PM, said:

Further, ask yourself why does a tuning fork have two prongs yet is considered a single point sound source?

 

 

Enthalpy post#89

If a tuning fork is alone in air, it's a bipolar souce.

Though, its bottom is commonly put on a wood part that radiates more strongly for being bigger - and sometimes at a resonator. The bottom (middle of the U shape) vibrates with a small displaceent that fits the wood part better. This movement can result in a monopole source if a resonator is used, often a quarterwave box.

 

 

The ouptut from a tuning fork can be biploar, quadripolar or more up to full spherical.

 

Clearly if there is a close plane or other boundary things will be different.

 

Here is a good discussion.

 

http://www.acs.psu.edu/drussell/publications/tuningfork.pdf

[Enthalpy]

So you see that sound is no faster in stainless steel.

Your two authors should have stated what kind of stainless. In martensitic and ferritic stainless, sound is minimally faster than in carbon steel. In the common austenitic, it's slower.

 

Anyway, you mixed up the material with the wave. "Bulk waves" is when the material can't change its lateral dimension because the the thickness is much bigger than half a wavelength in the metal, and then the stiffness isn't Young's modulus E any more, but it divided by 1-2*µ², Poisson's coefficient. Obviously not the case in a bell.

 

And from 1st of January to 31st of December, the modes of a bell are flexural. But you won't find a table of their speed because it depends on the frequency and thickness.

 

The sound of a bell isn't harmonic, that's perfectly known. The frequency of the perceived note is even absent from the spectrum. But no, these spectrum lines are not emitted by small nor by distinct areas of the bell. Each is emitted by the whole bell, which superposes many modes.

[studiot]

If you weren't so commited to attack me for reasons that I don't understand, I'm sure we could cooperate a great deal better.

 

This should not be contest as to who can pick the most holes.

[Function]

Hi everyone! I'm back with a question;

 

I missed a few posts, so it's probable that the answer to my question is already somewhere is this maze:

 

Imagine a hollow body of perfect revolution (let's say, for instance, a paraboloid as a result of a revolution of a parabola of the form [math]y=x^2[/math]).

Imagine the body produces a sound wave as a consequence of it being tapped.

 

Let the average sound waves outside the object follow the equation

[math]y=A\cdot \sin{\left(\frac{2\pi}{T}t\pm \frac{2\pi}{\lambda}x\right)}[/math]

 

What will the equation of the average sound waves inside the object look like? Or what would just the amplitude be?

Edited May 3, 2014 by Function

[rktpro]

I guess a sine wave with less amplitude.

[Function]

There has to be a special relationship between the two amplitudes, no?

Not just 'smaller'

[rktpro]

There has to be a special relationship between the two amplitudes, no?

Not just 'smaller'

Of course, a special relation would be there based on bulk modulas, gamma, volume of bell etc. Edited May 7, 2014 by rktpro

[Function]

We've been focussing on bell-shaped metallic objects since this thread was started.

Update: do you know those metallic rings to make like 'rounds' of e.g. mashed potatoes or whatever? They show us the same phenomenon: if you hold your ear outside the ring, you hear a clear sound; if you hold your ear inside this ring (which is btw open on both sides), you hear almost nothing.

 

I guess we can expand the subject, no longer being obliged to stick to bells.