Question

Please calculate the total transmission (I2/I1) of ultrasound intensity from medium 1 to medium 2 in the following situations: (a) medium 1 directly contacts with medium 2. The acoustic impedences are noted in the figures below. (b) medium 3 is inserted between media 1 and 2. The acoustic impedence of medium 3 is 6.6 MRayls. (c) If the medium 3 is air with an impedence of 0.0004 MRayls. The attenuation in all the media is negnected.

Answer 1

a )

Accostic impedance is R = ( z₂ - z₁ / z₂ + z₁ )²

R + T = 1

T = 1 - R

T = 1 - ( z₂ - z₁ / z₂ + z₁ )²

T = 4 z₂z₁ / ( z₂ + z₁ )²

T = 4 X 1.65 X 26.4 / ( 1.65 + 26.4 )²

T = 0.22

b )

T₁ = I₃ / I₁

= 4 X 6.6 X 26.4 / ( 6.6 + 26.4 )²

I₃ = 0.64 I₁

T₂ = 4 X 1.65 X 6.6 / ( 1.65 + 6.6 )²

= 0.64

I₂ / I₃ = 0.64

I₂ = 0.64 I₃

I₂ = 0.64 X 0.64 X I₁

I₂ / I₁ = 0.41

c )

z₃ = 0.0004 MRays

T₁ = 4 X 4 X 10^-4 X 26.4 / ( 4 X 10^-4 + 26.4 )²

T₁ = 1.5 X 10^-5

T₁ = I₃ / I₁ = 1.5 X 10^-5   

T₂ = 4 X 1.65 X 4 X 10^-4 / ( 1.65 + 4 X 10^-4 )²

I₂ / I₃ = 9.7 X 10^-4

I₂ = 9.7 X 10^-4 X I₃

I₂ = 9.7 X 10^-4 X 1.5 X 10^-5 X I₁  

I₂ / I₁ = 1.46 X 10^-8