Waves

📚The physics

A wave transfers energy without transferring matter. In a transverse wave the oscillation is at right angles to the direction of travel — water waves, light, all electromagnetic waves. In a longitudinal wave it is along the direction of travel, giving compressions and rarefactions — sound.

The quantities. Amplitude is the maximum displacement from the rest position. Wavelength is the distance between two adjacent points in phase. Frequency is waves per second, and period \( T = 1/f \). These are tied together by

which is really just speed = distance ÷ time in disguise.

What happens at boundaries. Reflection bounces the wave back, with the angle of incidence equal to the angle of reflection, both measured from the normal. Refraction is a change of speed on entering a new medium, which bends the wave and changes its wavelength — but never its frequency, which is set by the source. Diffraction is spreading through a gap or round an edge, and it is only noticeable when the gap is about the same size as the wavelength.

Light: reflection. A plane mirror gives an image that is the same size as the object, as far behind the mirror as the object is in front, laterally inverted, and virtual — the rays only appear to come from it, so it cannot be caught on a screen.

Light: refraction. Going into a denser medium light slows down and bends towards the normal; coming out it speeds up and bends away. The refractive index is \( n = \dfrac{\sin i}{\sin r} \).

Total internal reflection happens when light travelling from a denser to a less dense medium meets the boundary at more than the critical angle \(c\), where \( \sin c = 1/n \). Then none escapes and all of it reflects. This is how optical fibres carry light and internet traffic around bends, and why a diamond sparkles.

Lenses. A converging lens brings parallel rays to the principal focus. If the object is further from the lens than the focal length you get a real, inverted image that can be projected on a screen. If it is closer than the focal length you get a virtual, upright, magnified image — a magnifying glass. Learn to draw the two standard rays: one parallel to the axis that then passes through the focus, and one straight through the centre, undeviated.

Dispersion. A prism splits white light into a spectrum because each colour refracts by a different amount. Violet slows most and bends most; red bends least. Order: red, orange, yellow, green, blue, indigo, violet.

The electromagnetic spectrum, in order of increasing frequency and decreasing wavelength: radio, microwave, infrared, visible, ultraviolet, X-rays, gamma. They all travel at \( 3.0 \times 10^{8} \) m s\(^{-1}\) in a vacuum. Uses and dangers run in step with frequency — radio for broadcasting, microwaves for cooking and phones, infrared for heaters and remote controls, ultraviolet for sterilising and detecting forgeries, X-rays for imaging, gamma for sterilising and treating cancer. The higher-frequency ones carry more energy and are correspondingly more dangerous: UV causes skin cancer and eye damage, X-rays and gamma cause cell mutation.

Sound is a longitudinal wave and needs a medium — a ringing bell in a vacuum jar falls silent while remaining visible. In air it travels at roughly 330–350 m s\(^{-1}\), faster in liquids and faster still in solids. Higher frequency means higher pitch; larger amplitude means greater loudness. Humans hear roughly 20 Hz to 20 000 Hz; above that is ultrasound, used for medical scans and for sonar.