Wave properties review
| Property | Symbol | Unit | Meaning |
|---|---|---|---|
| Wavelength | λ | m | Distance between consecutive crests or compressions |
| Frequency | f | Hz | Waves per second |
| Period | T | s | Time for one wave; T = 1/f |
| Amplitude | A | m | Maximum displacement; related to energy |
| Wave speed | v | m/s | v = fλ |
The speed of a wave depends on the medium, not on frequency or amplitude. When a wave enters a new medium, its speed and wavelength change, but its frequency stays the same.
Wave interactions
Reflection
Waves bounce off boundaries. A wave reflecting from a fixed end (like a rope tied to a wall) is inverted. From a free end, it isn’t.
Refraction
Waves change direction when they enter a medium at an angle and change speed. Ocean waves refract as they approach a beach, bending to arrive nearly parallel to the shore.
Diffraction
Diffraction is the spreading of waves around obstacles or through gaps. It is greatest when the gap is about the same size as the wavelength.
- You can hear around corners because sound wavelengths (cm to m) are similar to doorways.
- You can’t see around corners because visible light wavelengths are tiny (400–700 nm).
- AM radio waves (hundreds of metres long) diffract around hills better than FM waves (about 3 m).
Interference and superposition
When waves overlap, their displacements add. This is the principle of superposition.
| Type | What happens | Result |
|---|---|---|
| Constructive | Crest meets crest | Larger amplitude |
| Destructive | Crest meets trough | Smaller amplitude or cancellation |
In 1801, Thomas Young shone light through two narrow slits and saw a pattern of bright and dark bands. This double-slit experiment proved light behaves as a wave.
Noise-cancelling headphones use destructive interference: they produce a sound wave that is the exact opposite of outside noise.
Standing waves
When two identical waves travel in opposite directions, they form a standing wave with:
- nodes: points that never move
- antinodes: points of maximum vibration
Guitar strings, organ pipes and microwaves all involve standing waves. For a string fixed at both ends, the fundamental wavelength is twice the string length.
Resonance
Every object has natural frequencies. If it’s pushed at one of them, its vibrations grow dramatically: resonance. Examples: a singer shattering a wine glass, pushing a swing at the right moment, and the 1940 Tacoma Narrows Bridge collapse (often attributed to resonance, though aerodynamic flutter was the main cause).
Polarization
Polarization restricts a transverse wave’s vibrations to one plane. Only transverse waves can be polarized. Polarized sunglasses block horizontally polarized glare reflected from water and roads.
The electromagnetic spectrum
Electromagnetic waves are transverse waves of oscillating electric and magnetic fields. All travel at the speed of light in a vacuum: c = 3.00 × 10⁸ m/s.
The electromagnetic spectrum, from longest to shortest wavelength (lowest to highest frequency and energy):
| Type | Wavelength range | Uses | Hazards |
|---|---|---|---|
| Radio waves | > 1 m | AM/FM radio, TV, MRI | Generally safe |
| Microwaves | 1 mm – 1 m | Cooking, cell phones, Wi-Fi, radar | Heating at high power |
| Infrared | 700 nm – 1 mm | Remote controls, thermal cameras, heat lamps | Burns at high intensity |
| Visible light | 400–700 nm | Sight, photography, fibre optics | Bright light can damage eyes |
| Ultraviolet | 10–400 nm | Sterilization, vitamin D, black lights | Sunburn, skin cancer |
| X-rays | 0.01–10 nm | Medical imaging, airport security | Ionizing; can damage DNA |
| Gamma rays | < 0.01 nm | Cancer treatment, sterilizing food | Highly ionizing; very dangerous |
Mnemonic: "Raging Martians Invaded Venus Using X-ray Guns."
Energy and frequency
Electromagnetic energy comes in packets called photons. Photon energy depends on frequency:
E = hf (h = 6.63 × 10⁻³⁴ J·s, Planck’s constant)
Higher frequency means more energetic photons. That’s why UV, X-rays and gamma rays can break chemical bonds and damage cells, but radio waves can’t.
Example: Find the wavelength of an FM radio station at 100 MHz.
λ = c ÷ f = 3.00 × 10⁸ ÷ 1.00 × 10⁸ = 3.00 m
Common mistakes
- Thinking frequency changes when a wave enters a new medium. Speed and wavelength change; frequency doesn’t.
- Thinking microwaves or radio waves are "radiation" in the dangerous, ionizing sense. Only high-frequency radiation is ionizing.
- Thinking longitudinal waves can be polarized.
Try it yourself
- A wave has a frequency of 250 Hz and wavelength 1.4 m. Find its speed.
- Calculate the frequency of red light with λ = 700 nm.
- Explain why you can hear a radio in another room but not see it.
- Rank in order of increasing photon energy: X-rays, radio, visible, ultraviolet.
(Answers: 350 m/s; 4.3 × 10¹⁴ Hz; sound diffracts around doorways, light doesn’t; radio < visible < ultraviolet < X-rays)
Quick recap
- v = fλ; speed depends on the medium.
- Waves reflect, refract, diffract and interfere.
- Superposition creates constructive and destructive interference and standing waves.
- The EM spectrum ranges from radio waves to gamma rays, all at speed c in a vacuum.
- Photon energy E = hf increases with frequency.