You are viewing a free preview of this lesson.
Subscribe to unlock all 10 lessons in this course and every other course on LearningBro.
A wave is a disturbance that transfers energy from one place to another without transferring matter. Understanding the fundamental properties of waves — and being able to describe them precisely using mathematical language — is essential for everything that follows in this topic.
Waves come in two fundamental types, defined by the relationship between the direction of oscillation and the direction of energy transfer.
In a transverse wave, the oscillations are perpendicular to the direction of energy transfer. If you flick a rope up and down, the wave travels horizontally along the rope while the particles of the rope move vertically. Light, water surface waves, and all electromagnetic waves are transverse.
In a longitudinal wave, the oscillations are parallel to the direction of energy transfer. Sound is the most important example. When a loudspeaker cone pushes forward, it compresses the air molecules in front of it, creating a region of compression (high pressure). As the cone pulls back, it creates a region of rarefaction (low pressure). These compressions and rarefactions propagate through the air, carrying energy to your ear.
A useful way to remember: in a longitudinal wave, the particles oscillate along the direction the wave travels (longitudinal — along).
Every wave can be described using a small set of measurable quantities.
Amplitude (A) is the maximum displacement of a particle from its equilibrium (rest) position. It is measured in metres (m). For a sound wave, greater amplitude means a louder sound. For a light wave, greater amplitude means greater intensity.
Wavelength (λ) is the distance between two consecutive points in phase — for example, from one crest to the next crest, or from one compression to the next compression. It is measured in metres (m).
Frequency (f) is the number of complete oscillations per second. It is measured in hertz (Hz), where 1 Hz = 1 oscillation per second. A tuning fork vibrating at 440 Hz completes 440 full cycles every second.
Period (T) is the time taken for one complete oscillation. It is measured in seconds (s). Frequency and period are reciprocals:
T=f1andf=T1
For example, if a wave has a frequency of 500 Hz, its period is T = 1/500 = 0.002 s = 2 ms.
Wave speed (v) is the distance travelled by the wave per unit time. It is measured in m s⁻¹. The fundamental wave equation links speed, frequency, and wavelength:
v=fλ
This equation applies to all waves. If you know any two of the three quantities, you can calculate the third.
Worked example: A sound wave in air has a frequency of 680 Hz and a wavelength of 0.50 m. Calculate the speed of the wave.
v = fλ = 680 × 0.50 = 340 m s⁻¹
This is consistent with the known speed of sound in air at room temperature.
Waves are commonly represented using two types of graph, and it is vital to distinguish between them.
A displacement–distance graph is a snapshot of the wave at a single instant. The x-axis shows position along the wave (in metres), and the y-axis shows displacement. From this graph you can read off the amplitude (maximum displacement) and the wavelength (distance between consecutive points in phase).
A displacement–time graph shows how a single point on the wave oscillates over time. The x-axis shows time (in seconds), and the y-axis shows displacement. From this graph you can read off the amplitude and the period (time for one complete cycle). From the period, you can calculate the frequency using f = 1/T.
A common error is to confuse wavelength and period. Wavelength comes from a displacement–distance graph; period comes from a displacement–time graph.
Phase describes the stage a point on a wave has reached in its cycle. It is measured in degrees (0° to 360°) or radians (0 to 2π).
Two points on a wave are in phase if they have the same displacement and are moving in the same direction at all times. They have a phase difference of 0° (or 360°, or any multiple of 360°). For example, two adjacent crests are in phase, separated by exactly one wavelength.
Two points are in antiphase (or completely out of phase) if they have a phase difference of 180° (π radians). When one is at maximum positive displacement, the other is at maximum negative displacement.
The phase difference between two points separated by a distance Δx along a wave of wavelength λ is:
Δϕ=λ2πΔx
Worked example: Two points on a wave of wavelength 0.40 m are separated by 0.10 m. Calculate the phase difference.
Δφ = (2π × 0.10) / 0.40 = π/2 radians = 90°
The points are a quarter of a cycle apart.
| Quantity | Symbol | Unit | Equation |
|---|---|---|---|
| Period | T | s | T = 1/f |
| Frequency | f | Hz | f = 1/T |
| Wave speed | v | m s⁻¹ | v = fλ |
| Phase difference | Δφ | rad | Δφ = 2πΔx / λ |
These relationships form the foundation for every wave calculation in A-Level Physics. Make sure you can rearrange each equation confidently and select the correct one for a given problem.