\displaystyle Z = \rho v

\displaystyle a = \frac{(Z_2 - Z_1)^2}{(Z_1 + Z_2)^2}

\displaystyle \lambda = \frac{v_w}{f}

Ultrasound — above 20 kHz. Made and detected by a piezoelectric transducer (it works as both speaker and microphone).
Acoustic impedance (Z) — density × speed of sound, in kg/(m²·s).
Intensity reflection coefficient (a) — the fraction of intensity reflected at a boundary. Big difference in Z → big reflection. Equal Z → no reflection. That's why gel is used: it removes the air gap (air's Z is tiny).
Imaging: echo time tells depth. You can't see details smaller than about one wavelength, and you can only scan to about 500λ deep. Higher frequency = more detail but less depth.
Doppler ultrasound measures blood speed. There's a double shift (blood receives as a moving observer, then re-sends as a moving source). The beat frequency between sent and returning waves gives the speed.
Therapy: 10³–10⁵ W/m² can shatter gallstones; diathermy (deep heating) at 10³–10⁴ W/m². Diagnostic scans use about 10⁻² W/m², which is safe.
Cavitation — vapor bubbles form and collapse. Used in ultrasonic cleaners (about 40 kHz).
Other uses: sonar (30–100 kHz), ranging devices, finding cracks in aircraft wings.

Medium	ρ (kg/m³)	v (m/s)	Z (kg/(m²·s))
Air	1.3	330	429
Water	1000	1500	1.5 × 10⁶
Blood	1060	1570	1.66 × 10⁶
Fat	925	1450	1.34 × 10⁶
Muscle	1075	1590	1.70 × 10⁶
Bone	1400–1900	4080	5.7–7.8 × 10⁶

Problem	Setup	Answer
Fat to muscle (Ex. 17.7)	Z_fat = 925 × 1450; a = (1.34 − 1.70)² / (1.34 + 1.70)²	1.34 × 10⁶; a = 0.014 (1.4% reflected)
7 MHz scan in tissue	λ = 1540 / 7 × 10⁶; depth = 500λ	0.22 mm detail; 0.11 m deep
2.50 MHz on blood at 20.0 cm/s toward probe (Ex. 17.8)	Blood receives 2,500,325 Hz; echo returns 2,500,649 Hz	Beat frequency 649 Hz

Common mistakes (Chapter 17): treating decibels as linear (doubling intensity adds 3 dB, it doesn't double the dB); using ln instead of log₁₀; using °C instead of kelvin in v = 331√(T/273); thinking higher frequency travels faster (speed depends on the medium only); using 2L for a closed tube (it's 4L) or allowing even harmonics in a closed tube; flipping the Doppler sign (approaching must give a higher frequency); forgetting that an echo travels there and back.