Water deformation subjected to ultrasound waves

[loophole]

Hello everyone, in one of my projects I am dealing with the following problem:

We have a tank filled of water. If we assumed that a focused ultrasond beam hit the water perpendicularly to the surface. How
can I calculate the displacement of the water surface? In particular, I am interested in finding a formula, which describes the profile of the water surface displaced. (hp: the ultrasound beam hit only a circular area with diameter d of the surface of the water)

If you have any suggestion, link or book on what to look for to solve this problem please let me know. I have looked in internet but I did not find anything about it, probably because I am missing the physical concept, which is behind this phenomenon.

Thanks for those who will answer.

 

[Baluncore]

Welcome to PF.
Assuming the water is of infinite depth, so there is no internal reflection.
The acoustic impedance of the air and of the water are not the same, so the incident ultrasonic wave will be partially reflected by the impedance mismatch at the water surface. The component that is transmitted into the water will move the surface of the water at the ultrasonic frequency.
https://en.wikipedia.org/wiki/Acoustic_impedance
https://en.wikipedia.org/wiki/Acoustic_wave#Reflection
https://en.wikibooks.org/wiki/Engineering_Acoustics/Reflection_and_transmission_of_planar_waves

 

[loophole]

Welcome to PF.
Assuming the water is of infinite depth, so there is no internal reflection.
The acoustic impedance of the air and of the water are not the same, so the incident ultrasonic wave will be partially reflected by the impedance mismatch at the water surface. The component that is transmitted into the water will move the surface of the water at the ultrasonic frequency.
https://en.wikipedia.org/wiki/Acoustic_impedance
https://en.wikipedia.org/wiki/Acoustic_wave#Reflection
https://en.wikibooks.org/wiki/Engineering_Acoustics/Reflection_and_transmission_of_planar_waves

HIi, that's great sorry for the late reply, I did not get the notification of your answer. Anyway. What you say is totally correct and I agree with it. However, I am still unsure how to calculate the profile of the water displaced.

Here is my idea:

1) find the presssure transmitted
2) let's assume that the acoustic wave is focused on a circular area of raidus r, when it incide on the water surface. therefore the water should deflect in this area.
3) Now the force that opposes to the profile deflection of the water is only the surface tension? or there are other forces I should take into account?
4) how should I model the surface tension? I imagine it as a force which keep together water molecules. Should I then create a force diagram for each molecule? Then calculate the displacement for each molecule?

I am not so familiar with surface tension, if you know any reference which discuss how to solve this kind of problem, would you send them to me?

thanks.

 

[Baluncore]

Welcome back to PF.
I do not believe that surface tension is an important consideration.
You will have a pressure wave with a known energy per square metre, that is incident on the water surface. Much of that energy will be reflected, the remainder will be transmitted forwards through the water.
Find the reflection coefficient, then compute the amplitude of the displacement as the wave energy passes through the water.
You will need to find the bulk properties of air and water.

 

[loophole]

Welcome back to PF.
I do not believe that surface tension is an important consideration.
You will have a pressure wave with a known energy per square metre, that is incident on the water surface. Much of that energy will be reflected, the remainder will be transmitted forwards through the water.
Find the reflection coefficient, then compute the amplitude of the displacement as the wave energy passes through the water.
You will need to find the bulk properties of air and water.

ok Thank you. I will try with that.