Sound question

[Function]

Hello everyone

 

I have a question I have stumbled upon.. well... playing with stuff.

In my bathroom, I have some sort of cup with a chalice-like-shaped 'cover' (see attachment)

The black boll is a solid metal ball at which I hold this 'cover'. The rest is, of course, hollow.

 

Now, I've experienced something rather strange; when I tap my finger on the hollow, metal part, keeping hold of the solid ball, it produces a sound - rather logic. The strange part is, that the sound is extremely loud (well, it IS extremely loud when held less dan 2 cm from my ear) at the outer sides (outside of this 'chaliceshape') and there is absolutely no sound in this chalice shape. (So if I put my ear almost in this chalice-shaped cover, I hear nothing, whereas when I hold the outer side close to my ear, the sound is very loud.

 

Same phenomenon occurs when it's being tapped on from the inside.

 

How does this come?

 

Thanks.

 

Function

[StringJunky]

I might guess the waves formed inside are destructively interfering with each other i.e. canclling each other out much more than the waves formed on the outside. Here's a link to more detail about constructive and destructive interference: http://www.phys.uconn.edu/~gibson/Notes/Section5_2/Sec5_2.htm

Edited March 8, 2014 by StringJunky

[Strange]

It might also be something to do with the wavelength of the sound (which might depend on the circumference, for example) being longer than the diameter of the thing...

[studiot]

I really like this thread, it shows some great scientific observation +1.

 

First the experimental evidence.

 

By using the stainless steel food mixer bowl I can confirm function's results.

 

Firstly by ear I can definitely tell that the sound is louder outside the bowl than inside.

 

So I repeated this using a sound level meter.

 

The ambient was recording around 60 dB.

 

Outside the bowl I was getting readings of 70 - 74 dB

 

Inside the bowl the sound level read 64dB

 

As to the explanation

 

I do not think it is an interference effect.

The bowl is a curved vibrating plate, more commonly known as a bell.

Unlike wind instruments there is no vibrating volume (column) of air generating the sound.

The sound is generated by direct vibrational modes of the bell and transferred to the air.

 

Being contained in a nearly enclosed space the air inside the bell will offer a much stiffer response than the external air.

So generation of the same pressure variation will take more energy inside than outside the bell.

or the same energy will generate a smaller response.

 

This will show up as different acoustic impedences inside and outside the bell.

[Function]

I really like this thread, it shows some great scientific observation +1.

 

First the experimental evidence.

 

By using the stainless steel food mixer bowl I can confirm function's results.

 

Firstly by ear I can definitely tell that the sound is louder outside the bowl than inside.

 

So I repeated this using a sound level meter.

 

The ambient was recording around 60 dB.

 

Outside the bowl I was getting readings of 70 - 74 dB

 

Inside the bowl the sound level read 64dB

 

As to the explanation

 

I do not think it is an interference effect.

The bowl is a curved vibrating plate, more commonly known as a bell.

Unlike wind instruments there is no vibrating volume (column) of air generating the sound.

The sound is generated by direct vibrational modes of the bell and transferred to the air.

 

Being contained in a nearly enclosed space the air inside the bell will offer a much stiffer response than the external air.

So generation of the same pressure variation will take more energy inside than outside the bell.

or the same energy will generate a smaller response.

 

This will show up as different acoustic impedences inside and outside the bell.

 

So Tibet monks should better be on the inside of the bell when they're ringing it, medically seen?

 

By the way, amazing what difference there is inside, compared to outside the bowl!

Edited March 9, 2014 by Function

[imatfaal]

Agree with studiot that this has little to do with interferenc. You can find videos on line of the vibration of a wine glass being driven at resonant frequency - it moves in and out in the x direction and in the opposite phase in the y direction in its simplest form

[Function]

I have found an additional problem (read: question). Let my formulation of the question be supported by the following image:

 

let's assume the bell-like object has the form of an infinitely long paraboloid, of which there is a 'real', solid, tangible part (the bell-like shape itself) and an infinite, imaginary part

 

Then there would be 4 types of zones:

• Zone A is the infinitely large zone inside this paraboloid, starting outside of the tangible part
• Zone B is the infinitely large zone outside this paraboloid, starting outside the tangible part
• Zone C is the zone inside this paraboloid, covering the inside of the tangible part, making it the only limited zone
• Zone D is the infinitely large zone outside this paraboloid, covering the outside of the tangible part

So, we've already noticed that, if [math]I_X[/math] is the intensity of the sound in zone X, [math]I_D>I_C[/math].

 

Additional questions:

• Will there be sound in zone A?
• Will there actually even be sound in zone B? I haven't treated sound waves yet, but my best guess would be that the sound waves run perpendicular to the tangent of a point on the paraboloid, making both zone A and zone B completely soundless
• Will [math]I_A<I_B[/math] or will [math]I_A=I_B[/math], as both zone A and B are outside of the tangible part?

I have discovered that this is a most interesting subject. Thanks already for the worthful replies.

Edited March 9, 2014 by Function

[studiot]

 

I have found an additional problem (read: question). Let my formulation of the question be supported by the following image:

 

Sorry this is too simplistic.

 

Note that I said that the vibrations are developed by the bell.

 

The bell has various modes of vibration which you can see from the images segment the bell into zones.

 

https://www.google.co.uk/search?q=vibration+modes+of+a+bell&tbm=isch&tbo=u&source=univ&sa=X&ei=2mQcU_q1OIbBhAeKs4FI&ved=0CEcQsAQ&biw=1280&bih=585

[Function]

 

Sorry this is too simplistic.

 

Note that I said that the vibrations are developed by the bell.

 

The bell has various modes of vibration which you can see from the images segment the bell into zones.

 

https://www.google.co.uk/search?q=vibration+modes+of+a+bell&tbm=isch&tbo=u&source=univ&sa=X&ei=2mQcU_q1OIbBhAeKs4FI&ved=0CEcQsAQ&biw=1280&bih=585

 

Ah, thanks

 

Sorry, but I can't help it:

Just tested it, btw, and it seems like my presumption in #7 was quite right: I_A<I_B.

I held the cupthing away from my ear (about an arm length) and when I pointed it away from my ear, the sound was louder, whereas it was more quiet when I pointed the cup towards my ear (placing my ear in zone A)

[studiot]

The ear is insensitive to the phase of soundwaves.

 

The sides of the bell will be launching spherical (not planar) soundwaves into the free air.

 

But some parts of the sides will be travelling one way and some in the opposite direction, due to overtones.

That is the vibration is segmented as in the picture.

 

These spherical waves diffract round the bottom of the bell.

 

So the soundfield underneath will depend upon its width.

There are likely to be zones of cancallation and zones of reinforcement in your area A.

 

Even with the finite element calculations shown in the google images bell calculations are far from an exact science.

[Enthalpy]

Hearing the sound much louder at less than 2cm distance is a clear indication of a near-field situation, where the emitting object is smaller than, say half a wavelength. Similar to a mosquito, whose noise vanishes quickly with distance.

 

Under these conditions, the inner interference is very efficient - and it is destructive, because the vibration pattern of a bell is symmetric. The first mode is just an ellipse deformation, the second has three pairs of antinodes where three move outwards when the other three move inwards, and so on for higher modes. The opposite speeds sum to zero sound effect.

[studiot]

I'm not sure what you are trying to say, here , enthalpy.

 

I am having to guess at the frequency of sound produced, but a typical tinkling sound (eg middle C) has a wavelength of 3/4 of a metre.

 

So how do you fit this into a bathroom cup or food processor bowl, to produce audio interference patterns?

 

Edit I should make this plain that I am talking about the wavelength in air and by fitting into the cup I mean into the air inside the cup.

 

The wavelength of a 440 Hz vibration in steel is getting on for 20 times as great, since the velocity of sound in air is around 340 m/sc and in steel around 6000 m/s.

Edited March 10, 2014 by studiot

[Function]

because the vibration pattern of a bell is symmetric.

 

Despite your explanation and the image proofs given by studiot, I still strongly doubt this: I'm still convinced of it that the waves are 'stronger' there where the clapper hits the bell; of course, this will be cancelled when the clapper hits the exact opposite side of the bell, but what if it only hits the bell once?

[studiot]

Sound is a periodic variation in pressure.

 

To see how this happens inside a bell, we should look at ahorizontal section, rather than a vertical one as function has drawn.

 

So to start the sequence at (1) we have a circular horizontal section, looking up into the bell.

This is excited by tapping smartly with a clapper.

 

The simplest response of the shell is to compress in one direction and elongate in another as in (2).

 

What does not happen, if the bell rings, is for opposite sides to simultaneously move in the same direction as in (3).

Opposite sides move in opposite directions.

 

So if we add some axes to (2) we find that thare is a zone of compression (shown shaded and +) and a zone of rarefraction (shown clear and -) in (4).

 

Further these are divided by axes, shown dashed, at 45 degrees to the normal ones.

 

Followed by this is a springback by the shell in the opposite directions as in (5).

So now the roles of compression and rarefraction are reversed. The compression zone becomes the rarefraction zone and vice versa.

 

The dashed axes can now be seen to be lines along which there is no change and correspond to principal axes, found in other areas of mechanics.

 

If we now consider the space either side of these dashed axes we can see that we can see that a half-wave is set up, centred on the dashed axes.

I have drawn one of these in (6)

 

As the shell springs back, it passes through the circular shape again and the half cycle in (6) returns to zero and inverts as the ellipse changes direction.

 

It can be seen that the length of this is half a wavelength.

 

However you should not think of this as showing sound intensity or loudness varying over the interior.

 

 

Now to ties this in with what I said before.

 

The size of my bowl makes the half wavelength about 0.2metres. Thus the resonant frequency of the air in the bowl is about 340/0.4 = 850Hz.

 

But this is being excited by a system ringing at about 1/20th this resonant frequency, namely the stainless steel shell.

 

So there is significant acoustic impedence mismatch between the systems.

 

The air outside the bell is free-field and has no resonant frequency so coupling is much more efficient.

 

If we could drive the air inside the bell at its resonant frequency it we would immediately measure an increase in loudness.

This would not be the case if the quietness inside were due to interference.

Edited March 11, 2014 by studiot

[Enthalpy]

I am having to guess at the frequency of sound produced, but a typical tinkling sound (eg middle C) has a wavelength of 3/4 of a metre. [...]

 

The wavelength of a 440 Hz vibration in steel is getting on for 20 times as great, since the velocity of sound in air is around 340 m/sc and in steel around 6000 m/s.

The frequency of a bell depends on the dimensions squared. It can be very different from 440Hz!

 

This is a bending mode! It doesn"t equal a size divided by a compression wave velocity!

The size of my bowl makes the half wavelength about 0.2metres. Thus the resonant frequency of the air in the bowl is about 340/0.4 = 850Hz.

 

But this is being excited by a system ringing at about 1/20th this resonant frequency, namely the stainless steel shell.

 

So there is significant acoustic impedence mismatch between the systems.

 

The air outside the bell is free-field and has no resonant frequency so coupling is much more efficient.

You apply a factor-of-20 from the compression wave's speed, but this would increase the frequency, not decrease!

 

Anyway, /20 and *20 are obviously both false. The frequency results from a flexural wave.

 

 

Despite your explanation and the image proofs given by studiot, I still strongly doubt this: I'm still convinced of it that the waves are 'stronger' there where the clapper hits the bell [...]

 

The waves propagate to the entire bell, and much more quickly so than the sound lasts.

Edited March 11, 2014 by Enthalpy

[studiot]

 

You apply a factor-of-20 from the compression wave's speed, but this would increase the frequency, not decrease!

 

Anyway, /20 and *20 are obviously both false. The frequency results from a flexural wave.

 

Thank you for spotting this correction. It does not alter the fact of acoustic impedence mismatch however.

 

The actual mode of ringing is as described in your post #11 and was stated to be the simplest available. Of course there are more complicated ones, and I look forward to your mathematical analysis of them.

 

Please also explain (as I have done) why the sound inside the bell is necessarily different from the sound outside.

Edited March 11, 2014 by studiot

[Enthalpy]

The destructive inetrference is more effective inside because of short distance and direct sight.

 

The mathematical aanlysis of a ring would be simple, with modes frequencies like N² but with integer N starting at N. A bell is more complicated because the dome adds stiffness. This raises the lowest modes more than the higher ones.

[studiot]

What is the difference between the waves inside the bell and outside?

 

Do they, for instance. have the same equation of motion or a different one?

Each side of the same thin shell making essentially the same motion must be capable of imparting the same energy to the air inside and outside, yet the sound is measurably louder outside, than inside. So where did the energy go?

Edited March 12, 2014 by studiot

[Enthalpy]

The inner and outer faces of the wall have essentially the same speed. I also expect a significant intensity at the inner face, but only near to it, which is difficult to observe... As soon as the observation point goes near the center, the zero sum reduces the intensity.

 

Near the rim, you hear the difference between the inner and outer faces, or very little.

 

At the outer face, you have the possibility to be farther from the rim, and near one of the four (for the lowest mode) antinodes, where the destructive effect of the out-of-phase antinodes is small.

[studiot]

 

Posted Yesterday, 10:52 PM

The inner and outer faces of the wall have essentially the same speed. I also expect a significant intensity at the inner face, but only near to it, which is difficult to observe... As soon as the observation point goes near the center, the zero sum reduces the intensity.

 

Near the rim, you hear the difference between the inner and outer faces, or very little.

 

At the outer face, you have the possibility to be farther from the rim, and near one of the four (for the lowest mode) antinodes, where the destructive effect of the out-of-phase antinodes is small.

 

 

 

I'm sorry but none of this makes any sense in relation to the questions I asked in post 18.

 

Are you saying, for instance, that there are standing waves in the air outside the bell?

 

Perhaps I didn't make this absolutely clear, I am asking you about the sound waves in the air inside the bell, compared to the sound waves in the air outside the bell.

[Enthalpy]

You shouldn't try to understand interferences in terms of energy nor power, since this is misleading. Pressure and air velocity are better tools when adding waves. For instance, if an interference in air produces a net zero pressure near a moving solid surface, this surface will transmit zero power to the air.

 

It's all correct, conserves energy and power and whatever you want. These are interesting notions (which mislead some people to imagine "gregarian bosons"), but need quite some time to grasp, and the net result is just that power and energy are inefficient tools at interferences, so they're a bit disappointing.

 

Yes, I mean waves in air.

 

Within the bell, the wave is essentially standing, yes - and this makes analysis in terms of energy little useful. Outside, a big fraction of the wave (fraction of air velocity) is a near-field wave; whether you want to call it a standing wave, I won't argue about it.

 

For all low modes of a bell, the wave is much longer in air than the solid's dimensions. This is why the lower modes decay slowly and the bell sounds for long - in addition to the shape that provides a good holding point. The higher modes radiate efficiently, provide a brilliant attack, and disappear quickly. It's because bending modes propagate faster at higher frequencies, and when the speed in the metal exceeds the speed in air, the wave is emitted efficiently.

 

But as the lower modes are emitted by a small object with a multipolar vibration mode, analysis as a plane wave and power is misleading rather than helpful.

[studiot]

 

You shouldn't try to understand interferences in terms of energy nor power, since this is misleading. Pressure and air velocity are better tools when adding waves. For instance, if an interference in air produces a net zero pressure near a moving solid surface, this surface will transmit zero power to the air.

 

It's all correct, conserves energy and power and whatever you want. These are interesting notions (which mislead some people to imagine "gregarian bosons"), but need quite some time to grasp, and the net result is just that power and energy are inefficient tools at interferences, so they're a bit disappointing.

 

 

I have no idea what this refers to.

 

 

 

Yes, I mean waves in air.

 

Within the bell, the wave is essentially standing, yes - and this makes analysis in terms of energy little useful. Outside, a big fraction of the wave (fraction of air velocity) is a near-field wave; whether you want to call it a standing wave, I won't argue about it.

 

Now we are getting somewhere. Thank you.

 

I haven't called the soundwave outside the bell a standing wave, nor do I want to.

 

For the simple reason it cannot be one.

 

The outside surface of the bell produces a travelling wave that moves away from the bell, spreading out in all directions into function's zone D.

 

Since this is indefinite free space (the experimental results are the same in a big field) there is nothing to cause a standing wave.

 

I don't recall saying this was a plane wave, although assuming this simplifies the theory.

 

Now I agree that there are nodes and antinodes in the air inside the bell (functions zone C).

Therefore there are standing waves inside the bell.

 

You have stated that these standing waves interfere with something.

 

Can you explain how standing waves interfere, since they are standing?

 

Travelling waves do indeed interfere with other travelling waves and those diffracting round the bottom of the bell from zone D into zone A will do just this.

 

 

and when the speed in the metal exceeds the speed in air, the wave is emitted efficiently.

 

I'm sorry, run this past me agian.

 

The metal is pushing the air, yet you say its speed exceeds that of the air.

Ergo the air molecules must pass through the walls of the bell for this to happen.

[Enthalpy]

Standing waves do interfere as well.

 

The speed of sound in the metal. It depends on the frequency, because these are bending waves. At higher frequencies, bending waves in the metal are faster than waves in air, so these are transferred efficiently to air. At lower frequencies, the ones that last in a bell, the transfer is less efficient.

 

Studiot, you obviously have had an acoustics course - but acoustics is more varied and subtle than a course. You can do better than polemics.

[studiot]

 

Studiot, you obviously have had an acoustics course - but acoustics is more varied and subtle than a course. You can do better than polemics.

 

 

So what have I said that was controversial?

 

*****************************************************************************************************************************************************

 

 

Function, I don't know if you are still following this thread but here is a simple experimental analogy to what is happening.

 

Take an ordinary bicycle pump.

Remove the handle, complete with shaft and piston.

 

Crank the shaft and piston backwards and forwards in the same motion that it would follow inside the pump sleeve.

 

Do you feel significant air resistance?

 

Now put the inner assembly back inside the pump sleeve and repeat the action.

 

What do you notice?

 

You should notice that there is a significant fixed resistance due to sidewall friction.

But there is also increasing resistance the more you compress the air inside.

 

This is because the air inside the pump is confined, whereas the free air in the atmosphere is not.

Just as I said in post#4 about the difference between the air inside and outside the bell.

 

This analogy is not exact but follows the same principles. The pump is rather more dramatic because the air in the bell is loosly confined whereas the air in the pump is tightly confined.

 

You can perform further experiment, this time on waves and resonance, with your pump.

Try to pump backwards and forwards at different rates and observe what happens.

Edited March 17, 2014 by studiot

[rktpro]

Studiot, can you measure the intensity on both sides when the apparatus is in water, A medium of higher bulk modulous?