\(P = I\,A{\text{wave}}\) where \(I\) is the intensity and \(A{\text{wave}}\) the area of the wavefront.
| Amplitude \(A\) | Maximum displacement of a particle from its equilibrium position. |
| Wavelength \(\lambda\) | Distance between two successive points that are in the same phase (e.g. crest‑to‑crest). |
| Frequency \(f\) | Number of complete oscillations per second (unit Hz). |
| Period \(T\) | Time for one oscillation; \(T=\dfrac{1}{f}\). |
| Wave speed \(v\) | Relation between the three quantities: \(v = f\lambda = \dfrac{\lambda}{T}\). |
| Intensity \(I\) | Average power transmitted per unit area; for mechanical waves \(I\propto A^{2}\) (AO2). |
When one end of a taut rope is moved up and down periodically, a transverse progressive wave travels along the rope.
v = \sqrt{\frac{T}{\mu}}
\] where \(T\) is the tension (N) and \(\mu\) the linear mass density (kg m\(^{-1}\)).
Compressing and releasing one end of a coiled spring creates a series of compressions and rarefactions that travel along its length.
v = \sqrt{\frac{k}{\mu}}
\] where \(k\) is the effective spring constant (N m\(^{-1}\)) and \(\mu\) the linear mass density.
A small vibrator placed at the centre of a shallow water tank generates circular wave‑fronts that spread radially.
| Aspect | Rope (Transverse) | Spring (Longitudinal) | Ripple Tank (Surface) |
|---|---|---|---|
| Particle motion | Perpendicular to propagation | Parallel to propagation | Vertical while wave travels horizontally |
| Typical medium | String or rope under tension | Coiled metal or plastic spring | Water surface (shallow) |
| Wave‑speed formula | \(v = \sqrt{T/\mu}\) | \(v = \sqrt{k/\mu}\) | \(v = f\lambda\) (measured) |
| Wave‑front shape | Straight line (in 2‑D view) | Plane (in 1‑D view) | Concentric circles |
| Visualisation | Visible transverse displacement | Visible compression/rarefaction spacing | Bright/dark fringe pattern on screen |
When the source and/or observer moves relative to the medium, the observed frequency changes:
\[
f' = f\;\frac{v \pm v{\text{s}}}{v \mp v{\text{o}}}
\]
Worked example (exam‑style):
\[
f' = 800\;\frac{340 + 30}{340 - 0}=800\;\frac{370}{340}=870\;\text{Hz}
\]
The pitch is higher because the source moves towards the observer.
\[
f' = 800\;\frac{340 - 30}{340}=800\;\frac{310}{340}=730\;\text{Hz}
\]
Key points for the answer:
Electromagnetic (EM) waves are transverse, travel at the speed of light \(c = 3.00\times10^{8}\;\text{m s}^{-1}\) in vacuum and do not require a material medium.
| Region | Typical wavelength \(\lambda\) | Typical frequency \(f\) |
|---|---|---|
| Radio | \(> 1\;\text{m}\) | \(< 3\times10^{8}\;\text{Hz}\) |
| Microwave | 1 mm – 1 m | 3×10⁸ – 3×10¹¹ Hz |
| Infrared | 700 nm – 1 mm | 3×10¹¹ – 4×10¹⁴ Hz |
| Visible | 400 nm – 700 nm | 4×10¹⁴ – 7.5×10¹⁴ Hz |
| Ultraviolet | 10 nm – 400 nm | 7.5×10¹⁴ – 3×10¹⁶ Hz |
| X‑ray | 0.01 nm – 10 nm | 3×10¹⁶ – 3×10¹⁹ Hz |
| Gamma | < 0.01 nm | \(>3\times10^{19}\;\text{Hz}\) |
\[
I = I_{0}\cos^{2}\theta
\]
where \(\theta\) is the angle between the light’s initial polarisation direction and the axis of the polariser.
The three laboratory demonstrations provide the experimental basis for the principle of superposition, which underpins:
Understanding how energy, phase and wave‑fronts are transferred in simple systems enables students to predict and analyse more complex wave phenomena required for the Cambridge 9702 examination.
\[
\lambda = \frac{\text{measured distance}}{\text{number of spacings}}
\]
\[
\frac{\Delta v}{v}= \sqrt{\left(\frac{\Delta f}{f}\right)^{2}+\left(\frac{\Delta \lambda}{\lambda}\right)^{2}}.
\]
Wave motion is a periodic disturbance that transports energy without a permanent displacement of the medium. The three classic laboratory demonstrations—transverse waves in a rope, longitudinal waves in a spring, and surface waves in a ripple tank—illustrate the essential characteristics required by the Cambridge syllabus: definition of a progressive wave, amplitude, wavelength, frequency, period, speed, intensity, wave‑fronts, and the direction of particle motion. Extending these ideas to the Doppler effect, the electromagnetic spectrum and polarisation connects mechanical wave concepts to the broader A‑Level curriculum, while the practical measurement technique develops the experimental skills needed for the 9702 exam.
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