Acoustics & Ultrasonics

Speed of Sound & Impedance

c = √(B/ρ); Z = ρc. Gas: c = √(γRT/M).

Medium

Bulk modulus B (GPa)

Density ρ (kg/m³)

R = (Z₂−Z₁)/(Z₂+Z₁); power reflected = R².

Z₁ (MRayl)

Z₂ (MRayl)

I = p²/(2ρc); SPL = 20·log₁₀(p/20µPa).

Acoustic pressure p (Pa)

ρc (Rayl)

Reflected (ultrasound): Δf = 2·f·v·cosθ / c.

Transmit f (MHz)

Target speed v (m/s)

Angle θ (°)

Sound speed c (m/s)

λ = c/f; near field N = D²/4λ; divergence sinθ = 1.22λ/D; depth = c·t/2.

Aperture D (mm)

Frequency f (MHz)

c (m/s)

Echo time t (µs) — for depth

Formula reference

Speed/impedance: c=√(B/ρ); gas c=√(γRT/M) (T in K, M in kg/mol); specific acoustic impedance Z=ρc (Rayl).

Reflection: pressure R=(Z₂−Z₁)/(Z₂+Z₁); intensity reflected R²; transmitted 1−R².

Intensity/dB: I=p²/(2ρc); intensity level 10·log₁₀(I/10⁻¹²); SPL 20·log₁₀(p/20µPa).

Doppler (reflected): Δf=2fv·cosθ/c.

Beam: λ=c/f; near-field length N=D²/4λ; far-field divergence sinθ=1.22λ/D; pulse-echo depth =c·t/2.