Physics: Light and sound

Both light and sound are forms of energy that travel as waves. A wave is a disturbance that transfers energy from one place to another without transferring matter. There are two main types of waves. Transverse waves, like light, have oscillations (vibrations) that are perpendicular (at 90°) to the direction of energy transfer. Longitudinal waves, like sound, have oscillations that are parallel to the direction of energy transfer, consisting of compressions and rarefactions. Key properties include: Amplitude (the maximum displacement from the equilibrium position), Wavelength (λ, the distance between two consecutive identical points on a wave), Frequency (f, the number of complete waves passing a point per second, measured in Hertz), and Period (T, the time taken for one complete wave to pass a point). The speed of a wave(v) is related to its frequency and wavelength by the wave speed equation: v = fλ.

Reflection occurs when light bounces off a surface. A smooth, shiny surface like a plane mirror reflects light in a predictable way. To describe this, we imagine a line drawn at 90° to the surface at the point where the light hits; this line is called the normal. The incoming ray of light is the incident ray, and the outgoing ray is the reflected ray. The Law of Reflection states that the angle of incidence (the angle between the incident ray and the normal) is equal to the angle of reflection (the angle between the reflected ray and the normal). An image formed by a plane mirror is virtual (it cannot be projected onto a screen), upright, laterally inverted (left and right are swapped), the same size as the object, and appears to be as far behind the mirror as the object is in front of it.

Refraction is the bending of light as it passes from one medium to another, for example, from air into glass. This happens because light travels at different speeds in different materials. It travels fastest in a vacuum, slightly slower in air, and slower still in denser materials like water or glass. When light enters a denser medium at an angle, it slows down and bends towards the normal. When it enters a less dense medium, it speeds up and bends away from the normal. The amount of bending is related to the material's refractive index (n), a measure of how much it slows down light. A higher refractive index means more bending.

When light travels from a denser medium to a less dense medium (e.g., from glass to air), it bends away from the normal. If you increase the angle of incidence, the angle of refraction gets bigger, until it reaches 90°. The angle of incidence that causes this is called the critical angle (c). If the angle of incidence is increased beyond the critical angle, the light no longer refracts out of the medium. Instead, it is completely reflected back into the denser medium. This phenomenon is called Total Internal Reflection (TIR). Two conditions must be met for TIR: 1. The light must be travelling from a denser medium to a less dense one. 2. The angle of incidence must be greater than the critical angle. This principle is vital for technologies like optical fibres used in broadband internet and keyhole surgery.

Lenses are curved pieces of glass or plastic designed to refract light in a predictable way. A converging (or convex) lens is thicker in the middle and causes parallel rays of light to converge at a single point called the principal focus or focal point. A diverging (or concave) lens is thinner in the middle and causes parallel rays to spread out as if they came from a focal point. The distance from the centre of the lens to the focal point is the focal length. By drawing 'ray diagrams' using a few key rules, we can predict the location, size, and nature of the image formed by a lens. Images can be real (can be projected onto a screen, like in a cinema) or virtual (cannot be projected, like the magnified image in a magnifying glass).

Sound is a mechanical wave, which means it needs a medium (a substance) to travel through. It cannot travel through a vacuum. Sound is produced by vibrations. These vibrations cause particles of the medium to vibrate back and forth, passing the energy along. In air, this creates a series of compressions (areas where particles are bunched together) and rarefactions (areas where particles are spread apart). Since the particle vibrations are parallel to the direction of energy transfer, sound is a longitudinal wave. The characteristics of a sound are related to the properties of its wave. The pitch of a sound is determined by its frequency; a high frequency gives a high pitch. The loudness (or volume) of a sound is determined by its amplitude; a large amplitude gives a loud sound. Sound travels at different speeds in different media: fastest in solids, slower in liquids, and slowest in gases.

An echo is a reflection of a sound wave. When a sound wave hits a hard, flat surface like a cliff face or a wall, it bounces back. If the surface is far enough away, you will hear the reflected sound as a distinct echo after you hear the original sound. This principle is used in technologies like SONAR (Sound Navigation and Ranging) to map the seabed or locate submarines. We can use echoes to measure the speed of sound. The relationship is the familiar `speed = distance / time`. However, for an echo, the sound travels to the reflector and back again, so the total distance travelled is twice the distance to the reflector. The formula becomes `Speed of sound = (2 × Distance to reflector) / time taken for echo`.