Ultrasound and Testing Applications

Ultrasound applications in non-destructive testing and physical diagnosis.

Conceptual context

Ultrasound is a mechanical pressure wave with frequencies far above human hearing. In non-destructive testing it is typically used between 0.5 MHz and 20 MHz in metals, producing wavelengths on the order of millimeters. That scale allows detection of internal discontinuities comparable to the wavelength and requires understanding how material response depends on acoustic impedance.

The inspection method emits a pulse, records the echoes, and reads the time and amplitude information from internal interfaces. The leaf's central variables are $v_{us}$ (propagation speed), $t_{vuelo}$ (time of flight), $d_{defecto}$ (defect depth), $Z_{ac}$ (acoustic impedance), and $R_{ac}$ (reflection coefficient). The material density $\rho_{mat}$ is also decisive in $Z_{ac}$.

🟢 Essential level

In a pulse-echo ultrasonic test, the transducer sends a short impulse into the material. The pulse travels through the part, reaches a discontinuity, and returns as an echo. The strongest echo may correspond to a back wall or a defect. The travel time of the echo is $t_{vuelo}$.

The defect depth is obtained because the pulse travels twice: outward to the defect and back. Therefore, the real distance is half of the distance that a wave would travel at the material speed during $t_{vuelo}$. This is why the depth formula includes the factor 1/2.

The acoustic impedance $Z_{ac}$ combines density $\rho_{mat}$ and speed $v_{us}$. If a defect is filled with air, the difference in $Z_{ac}$ between the material and air is enormous, which produces a very intense echo. If the defect is filled with a similar material, the echo may be weak or absent. This is why air-filled defects are easy to detect, while inclusions of dense material are difficult to see.

🔵 Formal level

Basic formulas

The main relationship of this leaf is:

Defect depth from time of flight

This equation shows how $d_{defecto}$ depends on $v_{us}$ and $t_{vuelo}$ with a factor 2 for the round trip.

The acoustic impedance of the medium is defined as:

Acoustic impedance of the medium

This equation shows that $Z_{ac}$ increases if density $\rho_{mat}$ or speed $v_{us}$ increase. In heavy metals, $Z_{ac}$ is very high; in light liquids, it is much lower.

Real student questions

• Why use gel instead of air? Because air has very low $Z_{ac}$ (400 Rayl) and reflects almost all the energy, while the gel ($Z_{ac}$ ≈ 1.6 MRayl) matches the impedance between the piezoelectric transducer ($Z_{ac}$ ≈ 30 MRayl) and the metal part ($Z_{ac}$ ≈ 45 MRayl). Without a couplant, the energy loss is so large that almost no pulse penetrates.

• Does a strong echo always mean a large defect? Not necessarily. Echo amplitude depends on $R_{ac}$, which can be large for an air-filled crack (very low impedance) even if its volume is small. An air micro-crack sometimes produces a stronger echo than a large solid inclusion.

• Why does $\rho_{mat}$ matter if depth only depends on $v_{us}$ and $t_{vuelo}$? Because $\rho_{mat}$ determines $Z_{ac}$ and modulates echo detectability. Moreover, $v_{us}$ and $\rho_{mat}$ are correlated in a material: if density increases (for example, due to compression or aging), $v_{us}$ may increase or decrease, and both changes affect $Z_{ac}$. A hardened material may look like the "same" steel, but $v_{us}$ has changed and depth calculations give erroneous results.

• What happens with very strong grain noise? Grain noise is acoustic scattering produced by the material's grain boundaries. It scatters the reflected pulse in all directions instead of sending it back toward the transducer. To reduce noise, a lower frequency is chosen (longer wavelength, less sensitive to grains), accepting a loss of spatial resolution. This is an example of a fundamental trade-off in measurement physics.

Final synthesis

Ultrasonic tests convert $t_{vuelo}$ into $d_{defecto}$ using $v_{us}$. Acoustic impedance $Z_{ac}$ and reflection coefficient $R_{ac}$ control which echoes are detectable and what information about defect type can be extracted.

Calibration with a block of the same material reduces errors from variations in $\rho_{mat}$ and $v_{us}$. In real problems, these calculations must be complemented with pulse-shape observation and cross-validation between multiple measurements to discriminate defects, inclusions, and material fluctuations.