Describe the uses of ultrasound in nondestructive testing of materials, medical scanning of soft tissue and sonar including calculation of depth or distance from time and wave speed

3.4 Sound – Ultrasound

Objective

Describe the uses of ultrasound in nondestructive testing of materials, medical scanning of soft tissue and sonar, and calculate depths or distances from the measured travel time using the appropriate speed of sound.

1. Core concepts of sound (IGCSE syllabus)

• Production of sound – A vibrating source (e.g., a tuning‑fork or loud‑speaker diaphragm) creates alternating compressions and rarefactions that travel through a medium as a longitudinal pressure wave.
• Longitudinal wave – Particle motion is parallel to the direction of propagation.
• Audible frequency range – 20 Hz – 20 kHz for the human ear.
• Speed of sound in air – Approximately 340 m s⁻¹ at 20 °C, but varies with temperature:

  \(v_{\text{air}} \approx 331 + 0.6\,T\) (m s⁻¹, T in °C)

• Amplitude ↔ loudness – Larger amplitude → greater pressure variation → louder sound.
• Frequency ↔ pitch – Higher frequency → higher pitch.
• Echo – The reflected part of a sound pulse when it encounters a surface or discontinuity.

2. Ultrasound – definition and basic principle

• Definition (required for IGCSE) – Sound with a frequency above the upper limit of human hearing (> 20 kHz).
• Optional note (extension) – In practice the frequencies used for the applications below lie in the megahertz (MHz) range.

All ultrasound applications share the same echo‑time method:

1. A piezoelectric transducer converts an electrical pulse into a short ultrasonic burst.
2. The burst travels through the medium until it meets a boundary where acoustic impedance changes.
3. Part of the burst is reflected back to the transducer and reconverted into an electrical signal (the “echo”).
4. The round‑trip travel time t is measured, and the distance to the reflecting surface is obtained from

   Depth (or distance) formula \( d = \dfrac{v\,t}{2} \)

   where v is the speed of sound in the specific medium.

3. Choosing the correct speed of sound

4. Applications of ultrasound

4.1 Nondestructive testing (NDT) of solids

• Purpose – Locate internal flaws (cracks, voids, inclusions) without damaging the component.
• Typical frequencies – 1 – 10 MHz (higher frequency → better resolution, lower penetration).
• Materials examined – Metals, composites, welds, ceramics.
• Information obtained – Position of the defect, approximate size, sometimes nature of the defect.
• Speed of sound – Use the value from the table (e.g., steel ≈ 5900 m s⁻¹).

Quick‑check question – “A steel rod is examined and the echo returns after 3.5 µs. Which speed of sound should you use for the calculation?” (Answer: 5900 m s⁻¹)

4.2 Medical ultrasound scanning

• Purpose – Produce real‑time images of soft‑tissue structures (organs, blood vessels, fetus).
• Typical frequencies – 2 – 15 MHz (higher frequencies give finer image detail).
• Speed of sound in soft tissue – 1540 m s⁻¹ (used for all routine diagnostic scans).
• Key features

  • Non‑ionising radiation → safe for repeated use.
  • Scanning is performed by moving the probe; echo intensity versus depth is displayed as a 2‑D B‑mode image.

4.3 Sonar (Sound Navigation and Ranging)

• Purpose – Determine water depth, locate underwater objects, aid navigation.
• Types

  • Active sonar – Emits a pulse and measures the return time.
  • Passive sonar – Listens only for sounds produced by other sources (not required for this objective).

• Typical frequencies – 10 kHz – 1 MHz (lower frequencies travel farther, higher frequencies give better resolution).
• Speed of sound in water – 1480 m s⁻¹ (fresh water) or 1500 m s⁻¹ (sea water).

5. Quantitative work – depth or distance calculations

Worked example 1 – NDT

A steel block is examined with an ultrasonic pulse. The echo from a crack returns after 4.2 µs. Find the depth of the crack.

1. Speed of sound in steel: \(v = 5900\ \text{m s}^{-1}\).
2. Convert time: \(t = 4.2\ \mu\text{s} = 4.2 \times 10^{-6}\ \text{s}\).
3. Depth: \(\displaystyle d = \frac{5900 \times 4.2\times10^{-6}}{2}= 0.0124\ \text{m}=12.4\ \text{mm}\).

Worked example 2 – Medical ultrasound

An echo from the boundary between two tissue layers arrives 0.00030 s after emission. Determine the depth of the boundary.

1. Speed of sound in soft tissue: \(v = 1540\ \text{m s}^{-1}\).
2. Depth: \(\displaystyle d = \frac{1540 \times 3.0\times10^{-4}}{2}= 0.231\ \text{m}=23.1\ \text{cm}\). (Typical for abdominal scans.)

Worked example 3 – Sonar depth sounding

A ship’s sonar emits a pulse that returns after 0.12 s. Calculate the water depth.

1. Speed of sound in seawater: \(v = 1500\ \text{m s}^{-1}\).
2. Depth: \(\displaystyle d = \frac{1500 \times 0.12}{2}= 90\ \text{m}\).

6. Safety considerations

• Medical ultrasound – Generally safe (non‑ionising). Prolonged exposure at very high intensities can cause tissue heating; clinical devices limit acoustic power.
• NDT ultrasound – High‑intensity pulses can cause heating or cavitation in liquids. Operators should:

  • Wear hearing protection.
  • Avoid looking directly at the transducer’s beam.

• Sonar – Powerful active sonar can affect marine life. On‑board safety:

  • Use hearing protection when near the transducer.
  • Follow local regulations on sonar use.

7. Experimental skills (AO3) – classroom activity

Goal: Measure the speed of sound in air using an ultrasonic echo method.

1. Equipment

   • Ultrasonic transducer & pulser/receiver (≈ 40 kHz).
   • Flat wooden board (reflector).
   • Measuring tape or metre rule.
   • Digital timer or oscilloscope with time‑base.
   • Tripod to hold the transducer at a fixed height.
   • Safety checklist (ear protection, avoid direct beam).

2. Procedure

   1. Set the distance s between transducer and board (e.g., 1.00 m). Record to the nearest millimetre.
   2. Connect the transducer to the pulser/receiver and emit a short burst.
   3. On the oscilloscope, use cursors to read the round‑trip time t (time between transmitted pulse and received echo).
   4. Repeat three times, record each t, and calculate the average.
   5. Calculate the speed of sound: \(v = \dfrac{2s}{t_{\text{avg}}}\).
   6. Extension – Plot distance (s) on the x‑axis and round‑trip time (t) on the y‑axis for three different distances. The slope of the best‑fit line equals \(2/v\); use it to obtain v graphically.

3. Data table

   Trial	s (m)	t (ms)	v = 2s/t (m s⁻¹)
   1	1.00	5.84	342
   2	1.00	5.86	341
   3	1.00	5.85	342

4. Evaluation points

   • Uncertainty in distance measurement (tape width, alignment).
   • Resolution of the timer/oscilloscope (usually ±0.01 ms).
   • Effect of air temperature – repeat the experiment at different temperatures and compare with \(v = 331 + 0.6T\).
   • Systematic error if the board is not perfectly perpendicular to the beam (reduces reflected intensity).

8. Comparison of ultrasound applications

9. Suggested diagrams (to be drawn by the teacher or added to the notes)

1. Schematic of an ultrasonic pulse travelling through a solid, reflecting from a flaw, and returning to the transducer (labels: transducer, pulse, flaw, travel time t, calculated depth d).
2. Cross‑section of a medical ultrasound probe scanning soft tissue, showing emitted pulses, echoes from successive tissue boundaries, and formation of a 2‑D B‑mode image.
3. Sonar depth‑sounding diagram: ship‑mounted transducer, emitted pulse, reflection from seabed, round‑trip time t and depth calculation.

10. Summary

• Sound is a longitudinal pressure wave; ultrasound is sound with > 20 kHz frequency.
• Core sound concepts (production, audible range, speed in air, amplitude‑loudness, frequency‑pitch, echo) are required for the IGCSE syllabus.
• All three ultrasound applications (NDT, medical imaging, sonar) use the echo‑time method and the formula \(d = vt/2\).
• Accurate depth calculations require:

  • Selecting the correct speed of sound for the medium (see Section 3).
  • Halving the measured travel time.
  • Consistent units and attention to significant figures.

• Safety: ultrasound is non‑ionising but high‑intensity beams can cause heating, cavitation, or hearing damage; appropriate protective measures are essential.
• Experimental skill: students should be able to plan, carry out, record, evaluate, and (optionally) graphically analyse an echo‑based measurement of the speed of sound in air.
• Extension material (frequency ranges, acoustic impedance) can be used for higher‑ability learners.