Impedance sends the echo home. Time is depth. Motion is Doppler. That is the whole craft.
For Sonographers · US physicists·7 min
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You will be able to
01Compute reflection from a Z mismatch.
02Turn round-trip time into millimetres at 1540 m/s.
03Read Doppler as speed, angle, and the PRF ceiling.
Chapter 01
Why anything comes back
Acoustic impedance is density times speed. A mismatch reflects a fraction of intensity: the square of Z2 minus Z1 over Z2 plus Z1. Soft tissue to air is almost a mirror — that is why gel exists. Soft tissue to bone is a bright echo and an acoustic shadow behind it.
No mismatch, no echo. No echo, no image.
Simulation
Acoustic impedance — Change the numbers; the scene follows.
Assume 1540 metres per second in soft tissue. Depth is speed times half the round-trip. Axial resolution is about half the spatial pulse length. A shorter pulse (more bandwidth, higher frequency) sharpens the axis and dies sooner in depth. That trade is every preset on the machine.
Simulation
Axial resolution — Change the numbers; the scene follows.
Variables
λ = 0.308 mm
Keep thisHigher frequency is not ‘better’. It is shallower and sharper.
The Doppler shift is proportional to speed and to the cosine of the beam-flow angle. At ninety degrees the shift vanishes — that is a geometry error, not absent flow. PRF must be at least twice the shift or the spectrum aliases. Angle, scale, and wall filter are the three lies a bad tracing can tell.
Simulation
Doppler shift — Change the numbers; the scene follows.
Variables
Δf = 1,623.4 Hz
Δf=c2vf0cosθ
Keep thisNever quote a speed from a 60-degree tracing as if it were 0.