13.1 Sound Propagation, Modes, Velocity, and Wavelength

The ASNT NDT Level II ultrasonic general exam opens with official UT topic 1, Review of Ultrasonic Techniques. Those items are not asking you to derive the wave equation. They ask whether you know what kind of wave left the crystal, how fast it travels in the material named in the stem, what its wavelength is, what happens when it hits an interface, and why the beam is not a laser pointer.

This chapter unpacks that review. Section 13.1 is the physics every later UT section assumes. Section 13.2 puts a transducer and couplant on the part and runs straight-beam (0°) work. Section 13.3 bends the beam with Snell's law and walks a weld with skip distance. The teaching baseline is the current UT general outline prior to 5 February 2027. After that date ASNT is scheduled to roll a four-domain outline (principles/techniques; materials/product forms; data/interpretation/reporting; training/certification/safety). Do not replace today's topic list with that future map. Mention it only as a calendar fact.

Industry practice is written around the same physics. ASTM E114 (straight-beam pulse-echo), ASTM E164 (contact ultrasonic examination of weldments), ASTM E797 (manual ultrasonic thickness), and ASME Boiler and Pressure Vessel Code, Section V, Articles 4 and 5 all assume a known mode, a known velocity, and a beam you can aim. They do not publish a secret ASNT velocity. If a stem gives a velocity, a thickness, or a frequency, use the number in the stem. Typical training values in this section are labeled typical.

Four modes the exam will name

A piezoelectric crystal does not emit "ultrasound" as one thing. It launches a mechanical wave whose particle motion relative to the direction of travel defines the mode. Sort the mode before you talk about skip distance or a DAC curve.

Keep the four names from collapsing into one another.

Longitudinal is the only bulk mode that can cross a liquid couplant or a water path. That is why an immersion tank and a contact gel both carry an L-wave, and why a shear wave is generated inside the solid by refraction or by a specially cut crystal — not by swimming through oil.

Shear is slower, so at the same frequency it has a shorter wavelength (next heading). Shorter λ is one reason weld procedures prefer shear once the wedge has killed the longitudinal wave. Shear cannot exist in the water column of an immersion test; any shear you use in immersion is born at the water–metal interface by mode conversion.

Rayleigh energy hugs the surface. A fingerprint of grease, a weld spatter ridge, or a machining groove will eat it. It is not a volumetric weld tool. A stem that says the wave "penetrates about one wavelength and follows the surface around a radius" is naming Rayleigh, not Lamb.

Lamb / plate waves are guided. They need two free surfaces a wavelength-scale distance apart. They are dispersive: change frequency or thickness and the velocity changes, and different modes travel at different speeds. That is the opposite of the bulk L and S waves this chapter treats as constant-velocity in a given material. Do not answer that Lamb waves are "just weak longitudinal waves" or that they always travel faster than L-waves.

If the stem says creeping wave or head wave, treat it as a near-surface longitudinal-related technique, not as a fourth bulk mode you invent a handbook speed for. If it says Love wave, that is a horizontally polarized surface mode you will almost never need on this general exam. Stay with L, S, Rayleigh, and Lamb unless the stem forces another name.

Velocity, frequency, and wavelength

The one equation you must be able to rearrange in any units is

v = f λ so λ = v / f and f = v / λ

v is the phase velocity of that mode in that material, not "the speed of sound" as a universal constant. f is the frequency of the pulse (nominal probe frequency if the stem does not give a spectrum). λ is the wavelength in that material and mode.

Units must match. A shop-friendly pair is inches per microsecond and megahertz, because 1 MHz = 1 cycle per microsecond:

λ (in) = v (in/µs) / f (MHz)

In SI, v in metres per second and f in hertz give λ in metres.

Worked example: λ = v / f

A 5.0 MHz longitudinal wave travels in carbon steel. The stem (or the typical training table) gives v_L = 0.233 in/µs, which is 5900 m/s.

λ_L = 0.233 in/µs ÷ 5.0 MHz = 0.0466 in

In SI: 5900 m/s ÷ 5.0×10⁶ Hz = 1.18×10⁻³ m = 1.18 mm.

Same probe frequency, same steel, shear at a typical v_S = 0.128 in/µs (3230 m/s):

λ_S = 0.128 / 5.0 = 0.0256 in ≈ 0.65 mm.

The shear wavelength is shorter because the shear velocity is smaller. Resolution ideas later in this chapter and in 13.2 start here: shorter λ, smaller reflectors you can hope to resolve, if attenuation and the pulse length allow it.

A second rearrangement. A procedure wants a longitudinal wavelength no longer than 0.10 in in a material whose table velocity is 0.250 in/µs (a typical aluminum L-wave).

f = v / λ = 0.250 / 0.10 = 2.5 MHz.

A 2.25 MHz probe is close; a 1 MHz probe is a longer wave and a worse small-reflector bet.

Velocity does not change when you change frequency in a non-dispersive bulk mode. A 2.25 MHz L-wave and a 10 MHz L-wave in the same homogeneous steel travel at the same v_L. What changes is λ, attenuation, near-field length, and beam spread. Candidates who answer "raise frequency to speed the wave up" have confused v with f.

Typical velocities — and why the procedure table wins

Training courses and older ASNT classroom notes recycle a short list. Use it when the stem does not give a number. The moment the stem, the calibration block stamp, or the written procedure gives a velocity, that number wins.

Handbooks scatter around these values — 0.230 versus 0.233 in/µs for steel L, 5850 versus 5920 m/s, 0.127 versus 0.130 in/µs for steel shear, 2670 versus 2730 m/s for acrylic. None of those is an unpublished ASNT exam secret. Heat treatment, alloy, temperature, and residual stress all move velocity a little. Thickness gaging of used pipe is only as good as the velocity you verified on a known thickness of that alloy.

Temperature is the field version of the same warning. Steel velocity falls as temperature rises; a hot vessel measured with a room-temperature velocity will read thick. Water in an immersion tank is not 1480 m/s if it is 40 °C. The general exam will not require a thermal-coefficient table. It will require you to know that velocity is a material-and-mode property, not a probe property, and that the table on the technique sheet outranks a number you memorized in class.

Acoustic impedance and what happens at an interface

Acoustic impedance is

Z = ρ v

where ρ is density and v is the velocity of the mode that is arriving. Steel is dense and fast, so its longitudinal Z is large (on the order of 45 MRayl). Water is about 1.5 MRayl. Air is about 400 Rayl, four orders of magnitude smaller. You do not need those MRayl figures as trivia. You need the ranking and the reflection rule.

For a plane wave at normal incidence, the amplitude reflection coefficient is

R = (Z₂ − Z₁) / (Z₂ + Z₁)

and the intensity (energy) reflection coefficient is R². If Z₂ = Z₁, R = 0 and the wave does not notice the joint. If Z₂ ≫ Z₁ or Z₂ ≪ Z₁, |R| → 1 and almost all the energy reflects.

Worked comparison: steel–air versus steel–water

Take Z_steel ≈ 45, Z_air ≈ 0.0004, Z_water ≈ 1.5 (same MRayl units).

Steel into air: R ≈ (0.0004 − 45) / (0.0004 + 45) ≈ −1. Intensity reflection ≈ 100%. Essentially no useful energy crosses a dry steel–air gap. That is why a 0° probe sitting on a dry mill scale does not see the backwall, and why a tight lamination or a planar crack perpendicular to the beam is a loud reflector.

Steel into water (or water into steel): R ≈ (1.5 − 45) / (1.5 + 45) ≈ −0.94. Intensity reflection is still about 88%. Only a fraction transmits. Immersion testing works because that fraction is repeatable and because the water path is itself the delay line. It does not work because water is impedance-matched to steel. Couplant in contact testing has the same job: displace air so the residual mismatch is water-like or glycerin-like, not air-like.

Transmission is whatever is not reflected, after you account for the impedance definition of the amplitude coefficient. The exam point is directional:

• Large mismatch → strong reflection, weak transmission. Steel–air, steel–gas porosity, a disbond with an air film.
• Closer match → weaker reflection, more transmission. A well-bonded solid–solid interface can be almost silent if Z is similar (some cladding, some diffusion bonds). That is why a lack of bond is an echo and a good bond can be a through-transmission or backwall-still-present argument — later chapters pick that up.

A phase inversion (the minus sign on R when the wave goes toward a lower Z) is why some A-scans show a backwall from steel into air flipped relative to an echo from a high-Z inclusion. If the stem does not mention phase, do not volunteer it. If it does, the inversion happens on reflection from a lower-Z second medium.

Oblique incidence adds mode conversion: part of a longitudinal wave becomes shear, and part of a shear wave becomes longitudinal, at angles Snell's law allows. Section 13.3 is built on that. At 0° (normal incidence) you do not generate a shear wave by refraction. Straight-beam work stays in the mode you launched.

Attenuation: absorption, scattering, and path

Attenuation is the loss of pulse amplitude as the wave travels, other than the simple geometric fact that the beam is a spreading cone. Three words the general exam expects you to keep separate:

1. Absorption. Mechanical energy becomes heat in the lattice. More path, more absorption. Higher frequency usually means more absorption in metals.
2. Scattering. Grain boundaries, inclusions, porosity, and graphite flakes redirect energy out of the useful beam. Scattering rises fast when grain size is a sizable fraction of λ. Coarse-grained austenitic welds, cast stainless, and some copper alloys eat high-frequency pulses. The Level II response is often lower frequency, not "more gain forever."
3. Beam spreading (geometric). Even a lossless medium delivers less intensity on axis as the far-field cone widens. Spreading is not a material property, but the A-scan does not care why the peak got shorter.

Attenuation increases with:

• Frequency (shorter λ, more scatter and usually more absorption)
• Path length (a long skip, a thick forging, a double-backwall multiple)
• Grain size / scatterers relative to λ

Attenuation decreases the signal from a deep reflector and from the backwall. That is why a 10 MHz probe that looks brilliant on a 6 mm sheet is a poor choice for a 200 mm forging, and why a procedure may require 2.25 MHz or 1 MHz on attenuative product. Gain can restore a number on the screen. It cannot restore a pulse that has already been scattered into grass.

Do not call every small echo "noise from attenuation." Grass from coarse grains is scatter. Electrical hash is not ultrasonic attenuation. A lost backwall with a clean mid-wall echo is a reflector (lamination, crack, unbond), not "the steel got attenuative in that one strip."

Near field and beam spread

A circular piston crystal does not launch a tidy cone from the wear face. Close to the probe the on-axis intensity oscillates through a series of maxima and minima. That region is the near field (Fresnel zone). The last on-axis maximum sits at the end of the near field. Beyond it, in the far field (Fraunhofer zone), amplitude falls smoothly and the beam spreads.

The training formula for near-field length of a circular crystal is

N = D² / 4λ which is the same as N = D² f / 4v

D is the effective crystal diameter. λ is the wavelength in the material the beam is traveling in (steel for a contact 0° probe after the wear face; water for the water path of an immersion probe).

Worked example: near field

A 0.50 in diameter, 2.0 MHz contact probe, longitudinal, typical steel v = 0.233 in/µs.

λ = 0.233 / 2.0 = 0.1165 in

N = (0.50)² / (4 × 0.1165) = 0.25 / 0.466 = 0.54 in

Same idea in SI. A 25 mm crystal, 2.0 MHz, steel 5900 m/s:

λ = 5900 / 2.0×10⁶ = 2.95 mm

N = (25)² / (4 × 2.95) = 625 / 11.8 ≈ 53 mm

What the formula says when you change one input:

Amplitude in the near field is a poor sizing reference. A small hole can look louder or quieter than an identical hole a few millimetres deeper just because you walked through a maximum or a minimum. Calibration reflectors and the zone of interest are preferably placed in the far field, or the procedure uses a dual probe / delay line so the near field lives in the delay, not in the thin wall. The last-maximum rule is also why some sensitivity peaks when the reflector sits near N — that is physics, not a reason to park every inspection there.

Beam spread in the far field is a cone. The half-angle to a stated intensity drop (first zero of a circular piston is often written with 1.22)

is of the form

sin γ = k λ / D

with k about 1.22 for the first zero, or a smaller handbook constant for a −6 dB or −3 dB edge. Do not treat 1.22 as an unpublished ASNT constant. Treat the direction:

• Lower frequency (larger λ) → more spread
• Smaller crystal → more spread
• Higher frequency, larger crystal → tighter beam

A 1 MHz, 6 mm crystal is a floodlight. A 5 MHz, 25 mm crystal is a flashlight. Spread is why a small-diameter angle-beam probe can illuminate a whole weld bevel — and why it can also pick up a corner trap you did not mean to see. Spread is also why the far-field amplitude falls even in a lossless metal: the energy is smeared over a larger wavefront.

Square or rectangular crystals, focused probes, and dual-element roof angles change the picture. If the stem says focused, the near-field formula above is not the whole story; energy is bunched at a designed focal depth. If it says dual, the two crystals are aimed to overlap a short distance below the surface (section 13.2).

Realistic exam scenarios

A stem gives 5.0 MHz, steel, and asks for longitudinal wavelength. Only 0.047 in / 1.18 mm matches λ = 0.233/5 (or 5900/5×10⁶). 0.233 in is the velocity, not λ. 1.165 in is v×f with the units abused. 0.026 in is the shear wavelength at the same frequency — the right arithmetic for the wrong mode.

A candidate claims shear waves inspect water-filled pipe from the inside because "ultrasound always shears." False. The water path is longitudinal. Shear, if used, is born in the steel wall.

A 10 MHz, 6 mm crystal is chosen for a 150 mm coarse-grained casting "for resolution." The near field in steel is short, but scatter destroys the pulse and the small crystal spreads. The procedure-correct move is usually a lower frequency and a larger crystal, then live with the longer λ.

A dry contact probe shows no backwall. The first fix is couplant and surface prep, not a new instrument. Z_air versus Z_steel is the whole story.

A Lamb-wave stem asks whether velocity is the steel handbook 0.233 in/µs. No. Plate-mode velocity is frequency- and thickness-dependent. Using a bulk L-wave table on a Lamb-wave clock is a thickness error waiting to happen.

A near-field item gives D = 0.50 in, f = 2.0 MHz, steel L, and four numbers. N = D²/4λ ≈ 0.54 in is the one that matches. D²/4v without converting frequency, or 4λ/D², are the usual distractors.

What Review of Ultrasonic Techniques physics items are really testing

If the stem names a mode, ask: particle motion, can it live in a liquid, and is it dispersive? If it names frequency and a material, write λ = v/f and pick the velocity for that mode. If it names an interface, write Z = ρv and ask how large the mismatch is — steel–air is a mirror. If it names amplitude loss, split absorption, scatter, and beam spread. If it names the region in front of the crystal, write N = D²/4λ and ask whether the reflector sits in the oscillating near field or the spreading far field. Those five questions are the physics half of official UT topic 1.