Exploring Structure Using Waves

Principles of Using Waves to Explore Structure

Waves can be used to explore the internal structure of objects and materials because they interact with boundaries between different materials. When a wave encounters a boundary, part of the wave is reflected back and part is transmitted through the boundary. This reflection and transmission depend on the properties of the materials involved.

Wave reflection and transmission: When a wave travelling through one material meets a boundary with another material, some of the wave energy is reflected back, and some passes through (transmitted). The amount reflected or transmitted depends on the difference in density or stiffness between the two materials.

Wave speed changes in different materials: Waves travel at different speeds depending on the material. For example, sound waves travel faster in solids than in liquids, and faster in liquids than in gases. This is because particles are closer together in solids, allowing vibrations to pass more quickly.

Using waves to detect internal features: By sending waves into an object and detecting the reflected waves (echoes), we can find internal features such as cracks, cavities, or different layers. The time taken for the echoes to return and their strength give information about the depth and nature of these features.

For instance, if a wave pulse is sent into a metal block and an echo returns after 0.002 seconds, and the speed of the wave in the metal is 5000 m/s, the distance to the internal feature causing the reflection is:

$$\text{Distance} = \frac{\text{speed} \times \text{time}}{2} = \frac{5000 \times 0.002}{2} = 5 \text{ m}$$

The division by 2 accounts for the wave travelling to the feature and back.

Ultrasound and Medical Imaging

Ultrasound waves are longitudinal sound waves with frequencies above 20,000 Hz, too high for humans to hear. They are widely used in medical imaging because they can travel through the body and reflect off boundaries between different tissues. Because they are longitudinal waves, they can effectively penetrate soft tissues and reflect at boundaries, making them ideal for imaging.

Reflection at boundaries inside the body: Ultrasound waves reflect when they meet boundaries between tissues with different densities or elastic properties, such as between muscle and bone or fluid and tissue. The reflected waves (echoes) are detected and used to create images.

Creating images from echoes: The time delay between sending the ultrasound pulse and receiving the echo shows how far away the boundary is. By scanning across the body and measuring many echoes, a 2D image of internal structures can be formed, such as a baby in the womb or organs.

For example, if an ultrasound pulse takes 0.0003 seconds to return from a boundary inside the body, and the speed of ultrasound in soft tissue is approximately 1540 m/s, the depth of the boundary is:

$$\text{Depth} = \frac{1540 \times 0.0003}{2} = 0.231 \text{ m} = 23.1 \text{ cm}$$

Seismic Waves and Earth's Structure

Seismic waves are waves generated by earthquakes or artificial explosions. They travel through the Earth and are used to study its internal structure.

Types of seismic waves:

• P-waves (Primary waves): Longitudinal (compressional) waves that travel fastest and can move through solids, liquids, and gases.
• S-waves (Secondary waves): Transverse (shear) waves that travel slower and can only move through solids.

Wave speed varies with Earth's layers: Seismic waves change speed and direction when they pass through different layers of the Earth because each layer has different density and state (solid or liquid). For example, S-waves do not travel through the liquid outer core, creating an S-wave shadow zone.

Using seismic data to infer internal structure: By analysing the arrival times and paths of seismic waves at different locations on Earth, scientists can map the size and properties of the Earth's core, mantle, and crust. Differences in wave speed and shadow zones reveal the presence of liquid and solid layers inside the Earth.

For example, if a P-wave takes 600 seconds to travel from an earthquake to a seismic station 7000 km away, the average speed of the P-wave is:

$$\text{Speed} = \frac{\text{distance}}{\text{time}} = \frac{7000 \times 10^3}{600} \approx 11,667 \text{ m/s}$$

Echo Sounding and Industrial Applications

Echo sounding uses sound waves to measure underwater distances and detect objects. It is widely used in marine navigation, fishing, and industrial inspections.

Use of sound waves underwater: A pulse of sound is sent from a ship or device into the water. The sound travels until it hits the seabed or an object and reflects back as an echo.

Measuring depth by echo time: The time taken for the echo to return is measured. Knowing the speed of sound in water (approximately 1500 m/s), the depth can be calculated using the formula:

$$\text{Depth} = \frac{\text{speed} \times \text{time}}{2}$$

Detecting objects and features: Echo sounding can locate underwater objects like shipwrecks or submarines and map the sea floor's shape. It is also used in industry to detect flaws inside materials by sending ultrasound waves and analysing echoes.

For example, if an echo returns after 0.1 seconds, the depth of the water is:

$$\text{Depth} = \frac{1500 \times 0.1}{2} = 75 \text{ m}$$