08 Ultrasound
Intensity transmission
T_I = 4 Z1 Z2 / (Z1 + Z2)². Energy conserved: R_I + T_I = 1 at a lossless interface.
Listen
Listen · English
Simulation
Intensity transmission — Change the numbers; the scene follows.
Where it works
Ultrasound
Transducer
At the transducer face — wavelength, pulse length, and the near/far field of the beam.
Open this machineFormula
Typical values
Variables
Results
R_I
Intensity reflection
0.4281
T_I
Intensity transmission
0.5719
R+T
Sum
1
Explanation
What it means
The amplitude transmission 2 Z2/(Z1+Z2) does not square to the intensity transmission because intensity is pressure × particle-velocity and the two media have different Z. The correct energy split is T_I = 4 Z1 Z2 / (Z1+Z2)², and it plus R_I equals 1. Soft tissue → bone reflects ~50% of intensity (R_I ≈ 0.5) and transmits the rest; tissue → air reflects 99.9%, which is why a gel is not optional. This is a working relation in Ultrasound.
Where it is used
Clinically it sits on the Ultrasound — Transducer. At the transducer face — wavelength, pulse length, and the near/far field of the beam. Ultrasound equations sit on the probe face and along the beam: impedance, Snell, Doppler, MI and TI. They explain why gel matters, why aliasing appears, and why a mechanical index is on the screen.
Ultrasound · Open this machineHow to use it
Enter Z1 and Z2 in MRayl. Presets: tissue/bone, tissue/air, tissue/gel, tissue/water. Read R_I, T_I and their sum (should be 1). Change one input and watch the curve and the simulation follow.
Symbols
- Z_1Impedance 11.63 MRayl
- Z_2Impedance 27.8 MRayl
Worked example
A typical case from the default values: Z_1 = 1.63 MRayl (Impedance 1); Z_2 = 7.8 MRayl (Impedance 2). Substituting into the relation gives R_I = 0.4281; T_I = 0.5719; R+T = 1. These are teaching numbers — align them with your machine.
Typical values give
- R_I = 0.4281
- T_I = 0.5719
- R+T = 1
Where it comes from
The displayed formula is the working relation. T_I = 4 Z1 Z2 / (Z1 + Z2)². Energy conserved: R_I + T_I = 1 at a lossless interface. Usual reference: Kremkau / Edelman. Derive it in the specialty lesson, then return here to pin the numbers.
Reference: Kremkau / Edelman
Assumptions & limits
Normal incidence, lossless interface, no mode conversion. Oblique incidence needs T and R for both compressional and shear (see Snell’s-law calculator). Gel Z is close to tissue, which is the point.
Pitfalls
Soft-tissue 1540 m/s is an assumption — not a measurement in that patient. Doppler angle 90° gives no shift. MI and TI are on-screen estimates, not absorbed dose. Normal incidence, lossless interface, no mode conversion. Oblique incidence needs T and R for both compressional and shear (see Snell’s-law calculator). Gel Z is close to tissue, which is the point.
Keep this
Gel, angle, and assumed speed of sound — get those three right before you trust a centimetre. Normal incidence, lossless interface, no mode conversion. Oblique incidence needs T and R for both compressional and shear (see Snell’s-law calculator). Gel Z is close to tissue, which is the point.
In this specialty