Physics: Light and sound

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 are where the particles of the medium oscillate perpendicular to the direction of energy transfer; examples include light and all other electromagnetic waves. Longitudinal waves are where the particles oscillate parallel to the direction of energy transfer; sound is a key example. Key properties of a wave 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, Hz), 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 equation: v = fλ.

Sound is a mechanical wave, which means it needs a medium (like air, water, or solids) to travel through; it cannot travel in a vacuum. It is a longitudinal wave, consisting of a series of compressions (areas of high pressure) and rarefactions (areas of low pressure). The two main properties of a sound we perceive are pitch and loudness. Pitch is determined by the frequency of the sound wave. A high frequency results in a high-pitched sound, while a low frequency results in a low-pitched sound. Loudness is determined by the amplitude of the sound wave. A wave with a large amplitude carries more energy and sounds louder, while a wave with a small amplitude sounds quieter. The typical range of human hearing is from 20 Hz to 20,000 Hz (20 kHz).

Reflection occurs when a wave, such as light, bounces off a surface. The Law of Reflection states that the angle of incidence(i) is equal to the angle of reflection (r), and that the incident ray, reflected ray, and the normal all lie in the same plane. The angles are always measured from the normal, a line perpendicular to the surface at the point of incidence. Refraction is the bending of light as it passes from one medium to another, for example from air to glass. This happens because light travels at different speeds in different media. The amount of bending is described by the refractive index(n) of the material. Snell's Law relates the angles of incidence and refraction to the refractive indices of the two media. When light enters a denser medium (e.g., air to glass), it slows down and bends towards the normal. When it enters a less dense medium (e.g., glass to air), it speeds up and bends away from the normal. If the angle of incidence in the denser medium is increased, the angle of refraction increases until it reaches 90°. The angle of incidence that causes this is called the critical angle (c). For any angle of incidence greater than the critical angle, the light does not refract out but is completely reflected back into the denser medium. This is called Total Internal Reflection (TIR).

Lenses are curved pieces of glass or plastic that refract light to form images. A converging lens (or convex lens) is thicker in the middle and causes parallel rays of light to converge at a point called the principal focus or focal point (F). A diverging lens (or concave lens) is thinner in the middle and causes parallel rays of light 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 (f). Ray diagrams are used to determine the position and nature of the image formed by a lens. The nature of an image is described as: real or virtual, inverted or upright, and magnified, diminished or same size. Real images can be projected onto a screen, while virtual images cannot. To draw a ray diagram, three key rays are used: 1) A ray parallel to the principal axis refracts through the focal point (for a converging lens) or appears to come from the focal point (for a diverging lens). 2) A ray passing through the centre of the lens continues undeviated. 3) A ray passing through the focal point before the lens refracts parallel to the principal axis (for a converging lens).

The electromagnetic (EM) spectrum is the range of all types of EM radiation. All EM waves are transverse waves that can travel through a vacuum at the same speed: the speed of light, approximately 3.0 x 10⁸ m/s. They differ from each other in their wavelength and frequency. The spectrum is continuous, but is conventionally divided into seven main regions, in order of increasing frequency (and decreasing wavelength): Radio waves, Microwaves, Infrared, Visible light, Ultraviolet, X-rays, and Gamma rays. A helpful mnemonic is 'Raging Martians Invaded Venus Using X-ray Guns'. As you move from radio waves to gamma rays, the frequency and energy of the waves increase, while the wavelength decreases. Each part of the spectrum has distinct properties, uses, and potential dangers. For example, radio waves are used for broadcasting, microwaves for cooking and communication, infrared for remote controls and thermal imaging, visible light for sight, ultraviolet for sterilisation (but can cause skin cancer), X-rays for medical imaging, and gamma rays for treating cancer.

When two or more waves meet at a point, they combine. The Principle of Superposition states that the resultant displacement at that point is the vector sum of the individual displacements. This can lead to two main effects: interference. Constructive interference occurs when two waves meet in phase, meaning their crests align with crests and their troughs align with troughs. The amplitudes of the waves add up, resulting in a wave with a larger amplitude. For sound, this results in a louder sound. For light, this results in a brighter spot. Destructive interference occurs when two waves meet in antiphase (or 180° out of phase), meaning the crest of one wave aligns with the trough of the other. The amplitudes cancel each other out. If the original waves had equal amplitudes, the resultant amplitude is zero. For sound, this results in a much quieter sound or silence. For light, this results in a dark spot. This phenomenon is responsible for the loud and quiet spots you can hear when two speakers play the same note, and the bright and dark 'fringes' seen in experiments with light.