Know that for a transverse wave, the direction of vibration is at right angles to the direction of propagation and understand that electromagnetic radiation, water waves and seismic S-waves (secondary) can be modeled as transverse
3.1 General Properties of Waves
Learning Objective
Students will be able to:
- State that in a transverse wave the direction of vibration is at right angles (90°) to the direction of propagation.
- Model electromagnetic radiation, water‑surface waves and seismic S‑waves (secondary waves) as transverse waves.
- Distinguish transverse from longitudinal waves and predict which media can support each type.
What Is a Wave?
A wave is a disturbance that carries energy from one location to another without the permanent transport of matter. The disturbance may be:
- a displacement of particles in a material medium (e.g., a rope, air, water), or
- a variation of a field, such as the electric‑magnetic (EM) field.
Wave Terminology
| Symbol | Quantity | Definition |
|---|---|---|
| λ | Wavelength | Distance between two successive points that are in the same phase (e.g., crest‑to‑crest or trough‑to‑trough). |
| f | Frequency | Number of complete cycles that pass a fixed point each second (unit: hertz, Hz). |
| T | Period | Time for one complete cycle; \(T=\dfrac{1}{f}\) (seconds). |
| A | Amplitude | Maximum displacement of the medium (or field) from its equilibrium position. |
| v | Wave speed | Rate at which the wave propagates; \(v=f\lambda\) (m s⁻¹). |
| k | Wave‑number | Spatial frequency; \(k=\dfrac{2\pi}{\lambda}\) (rad m⁻¹). |
| ω | Angular frequency | Temporal frequency; \(ω=2\pi f\) (rad s⁻¹). |
Mathematical Description of a Sinusoidal Wave
For a wave travelling in the +x direction the displacement (or field strength) y at position x and time t can be written as
\[
y(x,t)=A\sin\!\big(kx-\omega t\big)
\]
‑ kx gives the spatial variation (how the wave looks along the x‑axis).
‑ ωt gives the time variation (how the wave evolves).
The negative sign indicates propagation in the +x direction; a plus sign would describe a wave moving in the –x direction.
Worked Example – Speed of a Rope Wave
Given: frequency \(f=5\;\text{Hz}\), wavelength \(λ=0.40\;\text{m}\).
Find: wave speed \(v\).
\[
v = f\lambda = (5\;\text{Hz})(0.40\;\text{m}) = 2.0\;\text{m s}^{-1}
\]
Transverse Waves
A transverse wave is one in which the particles of the medium (or the fields) oscillate perpendicular to the direction in which the wave travels.
Common Transverse Waves
- Electromagnetic (EM) radiation – Light, radio waves, X‑rays, etc. The electric field E and magnetic field B oscillate at right angles to each other and to the direction of travel.
- Water‑surface waves – Particles move in (approximately) circular orbits: a dominant up‑and‑down motion (transverse) combined with a small forward‑backward component (longitudinal).
- Seismic S‑waves (secondary or shear waves) – Ground particles move side‑to‑side or up‑and‑down, perpendicular to the direction the wave front travels. S‑waves cannot travel through fluids because fluids cannot sustain shear stress.
Longitudinal Waves
In a longitudinal wave the particles vibrate parallel to the direction of propagation. The disturbance consists of alternating regions of compression (high density) and rarefaction (low density).
- Examples: Sound in air, compression waves in a slinky, seismic P‑waves (primary).
Transverse vs. Longitudinal – Quick Comparison
| Feature | Transverse | Longitudinal |
|---|---|---|
| Particle vibration direction | Perpendicular to propagation | Parallel to propagation |
| Typical examples | Light, water‑surface waves, S‑waves | Sound in air, P‑waves, spring compression |
| Medium requirement | Can travel in vacuum (EM) or any elastic solid/fluid (mechanical) | Requires a material medium that can be compressed |
| Energy transport mechanism | Oscillating fields or shear deformation | Compression‑rarefaction cycles |
Key Behaviour of All Waves
- Reflection – Wave returns into the original medium when it meets a boundary. Angle of incidence = angle of reflection.
- Refraction – Change in direction when a wave passes into a medium where its speed is different. Described by Snell’s law
\[
n{1}\sin\theta{1}=n{2}\sin\theta{2}
\]
where \(n\) is the refractive index.
- Diffraction – Bending of waves around obstacles or through apertures comparable in size to the wavelength.
Practical Illustration – Ripple‑Tank Experiment (IGCSE Practical)
- Generate circular waves with a point source (vibrating rod).
- Place a narrow slit in the tank. Observe straight‑line wave fronts beyond the slit – diffraction.
- Introduce a rectangular barrier at an angle. Reflected wave fronts demonstrate reflection.
- Insert a glass plate partially immersed in the water. The change in wave speed causes the wave fronts to bend – refraction.
By measuring the distance between successive crests (λ) and knowing the vibrator frequency (f), students can calculate the wave speed using \(v=fλ\), reinforcing the wave‑speed relationship.
Key Points to Remember
- The vibration direction of a transverse wave is at right angles (90°) to its direction of travel.
- Electromagnetic radiation is a transverse wave that does not need a material medium.
- Water‑surface waves are mainly transverse; particle motion is roughly circular.
- S‑waves are shear waves; they cannot propagate through liquids or the Earth’s outer core.
- Reflection, refraction and diffraction are observable for both transverse and longitudinal waves, and the ripple‑tank provides a visual demonstration.
Common Misconceptions
- “All waves are the same.” – Waves differ in particle motion (transverse vs. longitudinal) and in the media that can support them.
- “Light needs air to travel.” – Light is an EM transverse wave; it travels through vacuum as well as through transparent media.
- “Water particles travel with the wave.” – In surface waves each particle moves in a small orbit; the net horizontal displacement is negligible.
- “S‑waves can pass through the Earth’s outer core.” – The outer core is liquid and cannot sustain shear stress, so S‑waves are blocked (they are shadowed in seismograms).
Practice Questions
- Identify the wave type (transverse or longitudinal) for each phenomenon:
(a) A guitar string vibrating.
(b) A sound wave in air.
(c) A radio broadcast.
(d) A ripple on a pond.
- Explain why seismic S‑waves cannot travel through the Earth’s outer core.
- Draw a labelled sketch of a transverse wave on a rope, showing the direction of propagation and the direction of particle vibration.
- A ripple‑tank source produces waves of frequency 2 Hz. The measured wavelength is 0.30 m. Calculate the wave speed.
- Using Snell’s law, determine the angle of refraction when a light ray passes from air (n = 1.00) into water (n = 1.33) at an incidence angle of 30°.