Viscosity and resonant frequency?

[DrishantMaharjan]

Homework Statement

I'm doing my Physics Extended Essay for IBDP related to the variations of frequency in a Tibetan singing bowl with respect to depth, viscosity and temperature of liquid. While i can model the frequency of the bowl with respect to depth (using A.P. French's formula for wineglasses) However, for viscosity, I cannot for the love of god find a viable relationship theoretically. Can anyone help me out on this?

I am doing an experimental EE so i don't really know if this level of theoretical analysis would be necessary or not but either ways i thought i wouldn't hurt.

Moreover, for temperature I did find something but it's crazy hard for me to understand, if ya'll could dumb it down for me :") - the 'paper' in questions -> https://www.researchgate.net/profile/RaviWijesiriwardana/publication/316841293_Resonance_Frequency_Variations_of_Metallic_Tibetan_Singing_Bowl_with_Temperature/links/59131c520f7e9b70f498c1dc/Resonance-Frequency-Variations-of-Metallic-Tibetan-Singing-Bowl-with-Temperature.pdf

If ya'll can help me out in ANY way except these too (suggestions accepted), it would mean the world to me.

Relevant Equations

https://docs.google.com/document/d/13j2bIFgifZFLm65f4j6Wg9CI4sFxqEoDSIMCgCrWr9o/edit?usp=sharing

AP french's formula -> https://docs.google.com/document/d/13j2bIFgifZFLm65f4j6Wg9CI4sFxqEoDSIMCgCrWr9o/edit?usp=sharing
Temperature relation that i couldnt understand -> https://www.researchgate.net/profil...lic-Tibetan-Singing-Bowl-with-Temperature.pdf

 

[Steve4Physics]

Homework Statement: I'm doing my Physics Extended Essay for IBDP related to the variations of frequency in a Tibetan singing bowl with respect to depth, viscosity and temperature of liquidpdf

Hi @DrishantMaharjan. Welcome to PF. Here are some general points.

The correct citation for A.P. French’s paper is:
A.P. French, American Journal of Physics, 51, 688 (1983). "In Vino Veritas: A study of wineglass acoustics".

There is a pdf version here: https://www.nikhef.nl/~h73/tgo/praktgeluid/French1983.pdf

I found the other ‘paper’ (on temperature dependence) to be incomprehensible. Some of it appears not to make sense, e.g. showing a multimeter and microphone as the equipment used; complex equations appearing out of nowhere. It is not from a peer-reviewed journal and I would not use it.

I used to teach IB Physics and supervise EEs. In my opinion investigating the effects of 3 variables (amount, viscosity and temperature of liquid) in a limited timescale is too much. You need to discuss this with your supervisor before you start.

Note that if you change the liquid (to change the viscosity) you will also probably be changing the density. So you would need to distinguish between frequency changes due solely to viscosity and frequency changes due solely to density. Not sure it can be done easily.

If I were doing this EE, I would limit the investigation to the effects of a single (or no more than two) variable(s).

Good luck!

Edit - minor changes.

 

[DrishantMaharjan]

Hi @DrishantMaharjan. Welcome to PF. Here are some general points.

The correct citation for A.P. French’s paper is:
A.P. French, American Journal of Physics, 51, 688 (1983). "In Vino Veritas: A study of wineglass acoustics".

There is a pdf version here: https://www.nikhef.nl/~h73/tgo/praktgeluid/French1983.pdf

I found the other ‘paper’ (on temperature dependence) to be incomprehensible. Some of it appears not to make sense, e.g. showing a multimeter and microphone as the equipment used; complex equations appearing out of nowhere. It is not from a peer-reviewed journal and I would not use it.

I used to teach IB Physics and supervise EEs. In my opinion investigating the effects of 3 variables (amount, viscosity and temperature of liquid) in a limited timescale is too much. You need to discuss this with your supervisor before you start.

Note that if you change the liquid (to change the viscosity) you will also probably be changing the density. So you would need to distinguish between frequency changes due solely to viscosity and frequency changes due solely to density. Not sure it can be done easily.

If I were doing this EE, I would limit the investigation to the effects of a single (or no more than two) variable(s).

Good luck!

Edit - minor changes.

Hi thank you so much, I ended up looking at the AP french's formula however I focused on the derivation too. I ran into problem as I couldnt understand how they derived it. Could you help me out with that?

 

[TonyStewart]

opinion
--------

I would imagine a resonating bowl, bell or wine glass would behave like a standing wave element in electronics, except the radius from the stem to the rim and the dielectric is the surrounding air with a propagating speed in the vibrating medium. Adding fluid or sand reduces the radius to raise the pitch by reflecting the waves higher up from the base. Viscosity would dampen the waves like a resistor. Resonant modes could create aliasing or modulating interference with slightly different radius from the base. The Q of this resonant waveguide can be imagined from the return loss of the open-ended transmission line . Low return loss translates into very high Q and a long ring time as long as the base of the bowl or bell is not dampened by isolating it with a soft material or in the case of a wine glass with a long stem with no vibration at the base. Overtones could be complex with the velocity of air much lower than the waveguide.

 

[TonyStewart]

Further analogy of resonating bowls to electronic counterparts.
The article by French shows ω²= B/A which is identical to resonance of currents in inductors, L, out of phase with voltage for capacitors, C when connected in parallel and as always ω²=L/C But because the power is out of phase and stored, without resistance it simply stored resonant energy that would never decay. But for the singing bowls, the decay is very slow for many seconds as the viscous properties of air and the partial inelastic properties of metal behave as resistors which define the decay time, bandwidth and Q for both mechanical and electronic resonance structures. The shape of the physical structures with high symmetry help to mirror the 3D modes of motion into two modes of real (losses) and reactive into complex Euclidean geometric equations with several resonant frequencies likely shaped for harmonic characteristics and ratios of path length, height and diameter.

It is well known how metal acoustic velocities change with temperature but the damping factors of fluids should be expected to be resistive terminators that can change the standing wave ratios for tuning reflections and control the damping factor ζ or its inverse Q=1/2ζ with some vibration absorptive properties being Resistors. A simple explanation. https://engfac.cooper.edu/pages/tzavelis/uploads/Vibration Theory.pdf