Wave Physics

λ Wavelength in Two Media

λ₁ in Medium 1
— mm
λ₂ in Medium 2
— mm
λ = c / f

The wavelength scales with wave speed — a faster material yields longer wavelengths at the same frequency. The animation shows the spatial pressure pattern in each medium. Compressions move rightward; the ratio λ₂/λ₁ = c₂/c₁.

Immersion Testing

💧 Water Path Calculator

Must be ≤ material thickness

Required Water Path (WP)
— mm
WP = f − mp × (cₛ / cₚ)

Position the transducer face this distance above the material surface. The longer path in the faster solid "uses up" focal length equivalent to mp × cₛ/cₚ mm of water path.

cₚ default 1495 m/s ≈ water at 23 °C (±3 m/s per °C).

Beam Physics

🔭 Near-Field Distance

Near-Field Distance N
— mm
N = D² / (4λ) = D² ⋅ f / (4c)

Inspect at or beyond N for stable, predictable amplitude response. In the near field, constructive/destructive interference causes irregular amplitude variations that complicate flaw sizing.

Depth Sizing

⏳ Time-of-Flight → Depth

Depth (one-way)
— mm
d = (TOF × c) / 2

Enter the total round-trip time from the A-scan (transducer face to reflector and back). The result is the one-way depth. Divide by 2 because the pulse travels down and back.

Signal Loss

🔴 Attenuation Loss

Total Attenuation
— dB
Loss = α × f × d

Typical α (dB/mm/MHz): steel 0.3–1.5, aluminum 0.2–0.8, CFRP 1–5, HDPE 2–5, water 0.002. Coarse-grained castings can be 10× higher than wrought alloys.

Refraction & Mode Conversion

📈 Snell's Law & Critical Angle

Refracted Angle θ₂
— °
sin(θ₂) = (c₂/c₁) ⋅ sin(θ₁)

Default: water → steel (L-wave). For shear-wave wedge inspection use c₂ = 3200 m/s. “TIR” = total internal reflection (incident angle exceeds first critical angle).

Interface Analysis

🔄 Acoustic Impedance & Reflection

Z₁
—
Z₂
—
Reflection R
—
Transmission T
—
Z = ρc    R = [(Z₂−Z₁)/(Z₂+Z₁)]²

Default: water / steel. R and T are intensity coefficients (sum to 100%). A large impedance mismatch means most energy reflects — explaining why couplant is critical.

Beam Physics

🔍 Beam Divergence & Spread

Half-angle θ½ (−6 dB)
— °
Full Beam Spread
— °
sin(θ½) = 0.514λ/D    sin(θ) = 1.2λ/D

Half-angle θ½ is from the acoustic axis to the −6 dB pressure edge. Full beam spread = 2 × θ½. Larger diameter or higher frequency concentrates the beam. Near-field distance N is shown for context.

⚙ Wave Velocity from Material Properties

Calculates longitudinal (cL) and shear (cS) wave speeds from elastic constants. Useful when measuring new alloys or composites where tabulated values are unavailable.

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🖐 TOFD Crack Height Sizing

Computes crack height from the time difference between tip and base diffraction signals. Based on: a = cosθ × (Δt × v) / 2

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📎 Material Reference

Longitudinal wave speed, density, and acoustic impedance at room temperature.

Material cL (m/s) cS (m/s) ρ (kg/m³) Z (MRayl) α (dB/mm/MHz)
Steel (carbon)59003200780046.00.5–1.5
Aluminum 606163203130270017.10.2–0.8
Titanium Ti-6Al-4V60703110443026.90.3–1.0
Water (20°C)1480—9981.480.002
Water (23°C)1495—9971.490.002
Glycerin1920—12602.420.05
HDPE25009009502.382–5
CFRP (0° fiber)~7000—1550~10.91–5
Glass (borosilicate)56403280223012.60.1
Copper47002260890041.80.4
PZT-5A4350—775033.7—
Air (20°C)343—1.210.0004high

Values are approximate — always measure material-specific properties for critical inspections.