Determining energy delivered from critical angle

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SUMMARY

The discussion centers on calculating the critical angle for an ultrasound shock wave incident on a kidney stone in urine. The critical angle was determined to be 22° using the formula θc = arcsin(curine/cstone). To estimate the energy delivered to the kidney stone, the transmission coefficient must be applied, which relates to the intensity of the shock wave and the properties of the materials involved. The RMS intensity of the shock wave is given as 200 MW/m².

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  • Understanding of wave propagation in different media
  • Knowledge of critical angle calculations in acoustics
  • Familiarity with the transmission coefficient concept
  • Basic principles of energy transfer in ultrasound applications
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  • Learn how to calculate energy delivered using intensity and area
  • Explore the effects of material density and sound speed on ultrasound transmission
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Q. An ultrasound shock wave is incident on a kidney stone which is immersed in urine. Using the data below, calculate the critical angle at the urine-kidney stone interface, and thus estimate the energy that will be delivered to the spherical stone. Assume intensity is uniform across the stone.

\rho_{urine} = 1000kg/m^{3},<br /> c_{urine} = 1000m/s,<br /> \rho_{stone} = 2000kg/m^{3},<br /> c_{stone} = 4000m/s
Diameter of kidney stone d = 10mm
RMS intensity of shock wave I_{rms}=200MW/m^{2}

Attempt at an answer
I have been able to do the first part of the question. I calculated the critical angle as \theta_{c}=arcsin(c_{urine}/c_{stone})=22°

However, I don't know how to go from this to determining the energy delivered.

Thanks for any input.
 
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I don't know enough to answer the question, but I can see that you are missing some relevant equations. Do you have one for transmission coefficient?
 

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