Cambridge IGCSE Physics 0625 – 3.1 General Properties of Waves
3.1 General properties of waves
Objective
Describe what is meant by wave motion as illustrated by vibrations in ropes and springs, and by experiments using water waves.
What is a wave?
A wave is a disturbance that transfers energy from one point to another without the permanent transport of matter. The disturbance propagates through a medium (or, for electromagnetic waves, through space) by successive particle motions.
Key terminology
Term
Definition
Medium
The material (solid, liquid or gas) through which a wave travels.
Amplitude (A)
The maximum displacement of a particle from its equilibrium position.
Wavelength (λ)
The distance between two successive points in phase (e.g., crest to crest).
Frequency (f)
The number of complete cycles that pass a given point per second (Hz).
Period (T)
The time for one complete cycle; \$T = \frac{1}{f}\$.
Wave speed (v)
The speed at which the wave propagates; \$v = f\lambda = \frac{\lambda}{T}\$.
Vibrations in a rope
When one end of a taut rope is moved up and down, a transverse wave is produced. The particles of the rope move perpendicular to the direction of wave travel.
Increasing the tension \$T\$ in the rope increases the wave speed: \$v = \sqrt{\frac{T}{\mu}}\$, where \$\mu\$ is the mass per unit length.
Increasing the mass per unit length \$\mu\$ (e.g., using a thicker rope) decreases the wave speed.
The frequency of the source determines the frequency of the wave; the wavelength adjusts according to \$v = f\lambda\$.
Suggested diagram: A rope fixed at one end, the other end being oscillated by a hand. Show a crest moving away from the source.
Vibrations in a spring
Longitudinal waves can be demonstrated using a coiled spring. When one end of the spring is pushed and pulled, compressions and rarefactions travel along the spring.
Particle motion is parallel to the direction of wave travel.
The speed of a longitudinal wave in a spring depends on the stiffness \$k\$ and the linear density \$\mu\$: \$v = \sqrt{\frac{k}{\mu}}\$.
Changing the driving frequency changes the spacing of compressions (the wavelength) while the wave speed remains set by the spring’s properties.
Suggested diagram: A spring with alternating compressed and stretched sections moving away from a hand that oscillates the end.
Water‑wave experiments
Water waves provide a visual illustration of both transverse and longitudinal components. In a ripple tank or a shallow tray, a vibrator (e.g., a small paddle) creates circular wave fronts that spread outward.
Generating waves: The paddle is moved up and down at a steady frequency \$f\$.
Measuring wavelength: Place a ruler on the water surface and measure the distance between successive crests; this gives \$\lambda\$.
Determining wave speed: Use a stopwatch to record the time \$t\$ for a crest to travel a known distance \$d\$; then \$v = d/t\$. Verify that \$v = f\lambda\$.
Effect of depth: In shallow water, wave speed depends on depth \$h\$: \$v = \sqrt{gh}\$ (where \$g\$ is the acceleration due to gravity). In deep water, \$v\$ depends on wavelength: \$v = \sqrt{\frac{g\lambda}{2\pi}}\$.
Suggested diagram: Top view of a ripple tank showing concentric circular wave fronts emanating from a central point.
Summary of wave motion principles
Wave motion transfers energy without permanent displacement of the medium.
Key relationships: \$v = f\lambda\$, \$T = 1/f\$, and \$v = \sqrt{T/\mu}\$ for transverse rope waves or \$v = \sqrt{k/\mu}\$ for longitudinal spring waves.
Experimental observations (rope, spring, water) confirm these relationships and illustrate how tension, mass per unit length, stiffness, frequency and medium depth affect wave speed and wavelength.