Viscosity and resonant frequency?

In summary, viscosity refers to a fluid's resistance to flow, influenced by its internal friction, temperature, and composition. Resonant frequency is the natural frequency at which a system oscillates when disturbed. The relationship between viscosity and resonant frequency is significant in various applications, such as in fluid dynamics and material science, where changes in viscosity can affect the damping and frequency response of oscillatory systems. Understanding this relationship is crucial for designing systems that rely on fluid dynamics, such as in engineering and acoustics.
  • #1
DrishantMaharjan
2
0
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
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  • #2
DrishantMaharjan said:
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.
 
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Likes berkeman, WWGD, DrishantMaharjan and 2 others
  • #3
Steve4Physics said:
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?
 
  • #4
opinion
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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.
 
  • #5
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
 

FAQ: Viscosity and resonant frequency?

What is viscosity?

Viscosity is a measure of a fluid's resistance to flow. It describes how thick or thin a fluid is, with higher viscosity indicating a thicker fluid and lower viscosity indicating a thinner fluid. For example, honey has a higher viscosity than water.

How does viscosity affect resonant frequency?

Viscosity can affect the damping of oscillatory systems. In systems where a fluid's viscosity is a factor, higher viscosity typically results in greater energy dissipation, which can lower the amplitude of oscillations and slightly alter the resonant frequency by damping the system more effectively.

What is resonant frequency?

Resonant frequency is the natural frequency at which a system oscillates with the greatest amplitude. When a system is driven at its resonant frequency, it can absorb energy more efficiently, leading to larger oscillations. This concept is critical in various fields such as engineering, physics, and even medicine.

How do you measure viscosity?

Viscosity can be measured using instruments such as viscometers or rheometers. These devices typically measure the force required to move an object through the fluid or the rate at which the fluid flows under certain conditions, allowing for the calculation of viscosity.

Can resonant frequency be used to measure viscosity?

Yes, resonant frequency can be used to measure viscosity in certain contexts. For example, in a resonating viscometer, the change in the resonant frequency and damping of a vibrating element immersed in the fluid can be correlated to the viscosity of the fluid. This method is particularly useful for measuring the viscosity of small sample volumes.

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