Waves

Basic Properties of Waves

• Wavelength: Defined as the distance between the same points on two consecutive waves.

• Amplitude: Defined as the distance from the equilibrium line to the maximum displacement (which can be the crest or the trough).

• Frequency: The number of waves that pass a single point per second.

• Period: The time taken for a whole wave to completely pass a single point.

• Wave Equations:

  • $\text{velocity} = \text{frequency} \times \text{wavelength}$

  • $v = f \times \lambda$

  • $\text{period} = \frac{1}{\text{frequency}}$

  • $T = \frac{1}{f}$

  • In these equations, the period ($T$) is measured in seconds ($s$) and the frequency ($f$) is measured in hertz ($Hz$).

Fundamental Wave Relationships

• Velocity and Frequency: If the frequency increases, the velocity increases (for physics-only study).

• Velocity and Wavelength: If the wavelength increases, the velocity increases (for physics-only study).

• Period and Frequency: The period is inversely proportional to the frequency. A smaller period results in a higher frequency and a greater velocity (for physics-only study).

Classifications of Waves

• Transverse Waves:

  • Example: Light, or any electromagnetic wave.

  • Physical Characteristics: These waves have peaks and troughs.

  • Vibration Direction: Vibrations occur at right angles ($90^\circ$) to the direction of travel.

• Longitudinal Waves:

  • Example: Sound waves.

  • Physical Characteristics: These waves consist of compressions and rarefactions.

  • Vibration Direction: Vibrations are in the same direction as the direction of travel.

• Movement Principle: For both types of waves, it is the wave itself that moves, not the medium or material it passes through. For example, in a water wave, the wave moves, but the water does not keep moving forward with it.

Measuring Wave Velocity

• Measuring Sound in Air:

  • Echo Method: Create a noise approximately $50\,m$ from a solid wall. Record the time it takes for the echo to be heard, then calculate speed using $\text{speed} = \frac{\text{distance}}{\text{time}}$.

  • Datalogger Method: Place two microphones a large distance apart and connect them to a datalogger. Record the time difference as a sound passes from one microphone to the other, then use $\text{speed} = \frac{\text{distance}}{\text{time}}$.

• Measuring Ripples on Water Surfaces:

  • Stroboscope Method: Use a stroboscope set to the same frequency as the water waves. Measure the distance between the 'fixed' ripples shown by the strobe light and use $v = f \times \lambda$. Here, $v$ is wave speed in $m/s$, $f$ is frequency in $Hz$, and $\lambda$ is wavelength in $m$.

  • Pencil Method: Move a pencil along a piece of paper at the same speed as a wavefront. Measure the time taken to draw that line and use $\text{speed} = \frac{\text{distance}}{\text{time}}$.

Interactions of Waves at Material Boundaries

• Interaction Types (Physics Only): Waves can be reflected, absorbed, or transmitted at the boundary between two different materials.

• Reflection (Physics Only):

  • Waves reflect off flat surfaces.

  • Surface Texture: The smoother the surface, the stronger the reflected wave. Rough surfaces scatter light in all directions, appearing matt and non-reflective.

  • Law of Reflection: The angle of incidence is equal to the angle of reflection.

  • Opaque Objects: Light reflects if the object is opaque and the light is not absorbed. In this process, electrons absorb the light energy and then re-emit it as a reflected wave.

• Transmission (Physics Only):

  • Waves pass through transparent materials.

  • Transparency: The more transparent a material is, the more light passes through it.

  • Refraction: Light can still refract (bend) during transmission, but the overall process of passing through and emerging is transmission.

• Absorption (Physics Only):

  • Absorption occurs if the frequency of light matches the energy levels of the electrons in the material.

  • In this case, light is absorbed by the electrons and not re-emitted as light; instead, it is re-emitted over time as heat.

  • Color Perception: If a material appears green, it means only the green frequency has been reflected, while all other frequencies in the visible light spectrum have been absorbed.

Sound Waves and the Human Ear (Physics Only)

• Transmission through Solids: Sound waves can travel through solids by causing vibrations within the material.

• Mechanism of Hearing:

  • Outer Ear: Collects sound and channels it down the ear canal.

  • Ear Canal: The sound travels down as a pressure air wave.

  • Eardrum: A tightly stretched membrane that vibrates when hit by pressure waves. Compression forces the eardrum inward, while rarefaction forces it outward due to pressure changes. The eardrum vibrates at the exact same frequency as the incoming sound wave.

  • Small Bones (Stirrup): Connected to the eardrum, these bones vibrate at the same frequency and act as an amplifier for the sound waves received.

  • Inner Ear (Cochlea): Vibrations from the bones are transmitted to the fluid inside the cochlea. Compression waves are transferred to this fluid.

  • Cochlear Hairs: The cochlea is lined with small hairs, each originating from a nerve cell. As the fluid moves, these hairs move as well. Each hair is sensitive (attuned) to specific sound frequencies.

  • Neural Impulse: When a specific frequency is received, the corresponding hair moves significantly, releasing an electrical impulse to the brain, which interprets it as sound.

Limitations of Human Hearing (Physics Only)

• Audible Range: Humans generally cannot hear frequencies below $20\,Hz$ or above $20\,kHz$.

• Loss of High Frequencies: Hairs in the cochlea attuned to high frequencies are often the first to die or be damaged. Causes include:

  • Constant exposure to loud noise over many years.

  • Changes in the inner ear due to the natural aging process.

  • External factors such as smoking, chemotherapy, and diabetes.

• Evolutionary Advantage: Humans evolved this specific range because it provides the greatest survival advantage. Humans do not hear ultrasound because we rely on accurate vision rather than sonar for hunting.

Ultrasound and Infrasound (Physics Only)

• Ultrasound Definition: Sound waves with frequencies higher than the upper limit of human hearing (> 20\,kHz).

• Behavior at Boundaries: When ultrasound reaches a boundary between two different media, it is partially reflected. The remainder of the wave continues through the material.

• Applications of Ultrasound:

  • Distance calculation: By measuring the time between emission and detection of reflected waves (given constant speed), the distance to a boundary can be determined.

  • Industrial Imaging: A crack in a metal block causes waves to reflect earlier than expected, revealing internal flaws.

  • Medical Imaging: Used for non-invasive scanning of a human foetus.

  • Sonar: Ships send ultrasound pulses to calculate depth or locate shoals of fish by timing reflections from the seabed.

• Infrasound (Seismic Waves): Sound waves with frequencies lower than $20\,Hz$. They are used to explore the Earth's core. There are two types:

  • P Waves (Primary): Longitudinal waves that can pass through both solids and liquids.

  • S Waves (Secondary): Transverse waves that can only pass through solids. They travel slower than P waves.

  • Discovery of Earth's Core: On the exact opposite side of the Earth from an earthquake, only P waves are detected. The absence of S waves suggests the Earth has a liquid core that S waves cannot penetrate.

Electromagnetic (EM) Waves

• General Properties:

  • They are transverse waves.

  • They do not require particles/medium to move.

  • In a vacuum (space), all EM waves travel at the same velocity (the speed of light).

  • They transfer energy from a source to an absorber (e.g., a microwave source to food, or the Sun to the Earth).

• Relationships:

  • Because speed is constant, if the wavelength decreases, the frequency must increase.

  • As frequency increases, the energy of the wave increases.

• The Human Eye: The retina can only detect visible light, which is just a small portion of the total EM spectrum.

• Refraction:

  • Entering a denser material: The wave slows down and bends towards the normal.

  • Entering a less dense material: The wave bends away from the normal.

  • Wavefronts: Horizontal lines representing the maxima of transverse waves. In denser materials, both speed and wavelength decrease.

• Differential Interactions: Substances interact differently with EM waves based on wavelength:

  • Glass: Transmits/refracts visible light, absorbs UV radiation, and reflects IR radiation.

• Dispersion: White light disperses into a spectrum (rainbow) in a prism because different wavelengths refract by different amounts. Shorter wavelengths (like blue light) slow down more and refract more than longer wavelengths (like red light).

Radio Waves and Atomic Radiation

• Production of Radio Waves: Generated by oscillations in electrical circuits.

• Absorption of Radio Waves: When absorbed, they create an alternating current (AC) in a circuit at the same frequency as the radio wave.

• Atoms and EM Radiation:

  • Absorption: Occurs when an electron moves to a higher orbit, further from the nucleus.

  • Emission: Occurs when an electron falls to a lower orbit, closer to the nucleus.

  • Ionization: If an electron gains sufficient energy, it can leave the atom entirely to form an ion.

  • Gamma Rays: These originate from changes specifically in the nucleus of an atom.

Hazards and Uses of Electromagnetic Waves

• Hazards:

  • Harm depends on the type of radiation and the radiation dose (the amount of exposure).

  • UV Light: Causes premature skin aging and increases the risk of skin cancer. Sun cream is used for prevention.

  • X-rays and Gamma Rays: These are types of ionizing radiation. They can cause gene mutations which lead to cancer. Exposure must be minimized.

• Specific Uses:

  • Radio: Used for TV and radio because long wavelengths can travel far without losing quality.

  • Microwave: Used for satellite communication (can penetrate the atmosphere) and cooking food.

  • Infrared (IR): Used for cooking and infrared cameras because it transfers thermal energy.

  • Visible Light: Used in fibre optics because it provides the best reflection and scattering within glass compared to other wavelengths.

  • Ultraviolet (UV): Used for sun tanning and energy-efficient lamps; it radiates less heat but more energy than visible light.

  • X-rays and Gamma Rays: Used for medical imaging and cancer treatment because they are very high energy and penetrate materials easily.

Lenses (Physics Only)

• General Rules:

  • Light passing through the exact center of the lens does not change direction.

  • Lenses are represented in diagrams by a dashed vertical line.

  • Focal Points: Points on either side of the lens where light can converge.

• Concave Lenses:

  • Shape: "Caves" inward; thinner at the center than at the edges.

  • Effect: Spreads light outwards (diverging). Light appears to have originated from the focal point.

  • Ray Diagram for Concave: Draw a horizontal ray from the object top to the lens, then a faint line from the focal point to that contact point; the ray exits following the direction of the faint line.

  • Images: Can only have virtual images.

  • Use: Correcting short-sightedness (where light focuses in front of the retina) by spreading light out so it focuses on the retina.

• Convex Lenses:

  • Shape: Wider at the center.

  • Effect: Focuses light inwards (converging). Horizontal rays focus onto the focal point.

  • Images: Can produce either virtual or real images. Real images appear on the opposite side of the lens from the object; virtual images appear on the same side.

  • Use: Magnifying glasses, binoculars, and correcting long-sightedness (by focusing rays closer).

• Magnification Formula:

  • $\text{magnification} = \frac{\text{image height}}{\text{object height}}$

Visible Light and Color (Physics Only)

• Spectrum: Each color has a narrow band of wavelength and frequency. Blue has a shorter wavelength and higher frequency than red.

• White Light: Sunlight is a mixture of all colors, which appears white.

• Types of Reflection:

  • Specular: Reflection off a smooth surface giving a single, clear reflection.

  • Diffuse: Reflection off a rough surface causing scattering.

• Color Filters: Work by absorbing all colors except the specific wavelength (color) they are intended to let through.

• Opaque Colors: The color of an opaque object is determined by which wavelengths it reflects most strongly. Wavelengths not reflected are absorbed.

  • White: Reflects all wavelengths.

  • Black: Absorbs all wavelengths.

• Transmitting Objects: Objects that let light through are either transparent or translucent (translucent objects scatter most light, letting only some through).

Black Body Radiation and Earth (Physics Only)

• Infrared Emission: All objects, regardless of temperature, emit and absorb IR radiation.

• Temperature Effects:

  • Hotter Bodies: Release a greater amount of radiation per second (more power) and release more shorter-wavelength (higher energy) radiation.

• Black Bodies: An object that absorbs all radiation it receives (no reflection or transmission) and therefore emits all types of radiation.

• Temperature Equilibrium:

  • Constant Temperature: The body absorbs radiation at the same rate as it emits it.

  • Increasing Temperature: The body absorbs more energy than it emits.

  • Cooling Down: The body releases energy at a greater rate than it absorbs.

• Earth's Temperature: Temperature is determined by the balance of energy absorbed from the Sun and energy re-radiated. The atmosphere maintains constant temperature by absorbing IR from the Sun and trapping IR re-radiated from the Earth's surface.