Progressive Waves – Cambridge A‑Level Physics 9702
1️⃣ What is a Progressive Wave?
A progressive wave is a disturbance that travels through a medium, carrying energy from one place to another without transporting matter. Think of a ripple moving across a pond when you drop a stone – the water itself doesn’t move far, but the wave does.
2️⃣ Transverse vs. Longitudinal Waves
- 🔵 Transverse wave – particle displacement is perpendicular to the direction of propagation. Example: waves on a string or electromagnetic waves.
- 🔴 Longitudinal wave – particle displacement is parallel to the direction of propagation. Example: sound waves in air.
3️⃣ Graphical Representation
On a graph, the horizontal axis usually represents position (x) or time (t), while the vertical axis shows the displacement (y) or pressure (p).
Transverse Wave Example
\$y(x,t)=A\sin(kx-\omega t)\$
- \$A\$ – amplitude (maximum displacement)
- \$k=\frac{2\pi}{\lambda}\$ – wave number (related to wavelength \$\lambda\$)
- \$\omega=2\pi f\$ – angular frequency (related to frequency \$f\$)
Longitudinal Wave Example
\$p(x,t)=p_0 + \Delta p \sin(kx-\omega t)\$
- \$p_0\$ – ambient pressure
- \$\Delta p\$ – pressure amplitude
4️⃣ Key Relationships
| Quantity | Formula |
|---|
| Wave speed | \$v = f\lambda = \frac{\omega}{k}\$ |
| Frequency–period relation | \$f = \frac{1}{T}\$ |
| Energy per unit volume (transverse) | \$E = \frac{1}{2}\mu \omega^2 A^2\$ |
5️⃣ Exam Tips Box
🔍 Remember: - Identify whether the wave is transverse or longitudinal from the diagram.
- Use the correct formula for wave speed: \$v = f\lambda\$ or \$v = \frac{\omega}{k}\$.
- Check units – metres per second (m/s) for speed, hertz (Hz) for frequency.
- When asked for amplitude, look for the maximum displacement from the equilibrium line.
- For energy questions, use the appropriate energy density expression.
|
6️⃣ Practice Questions
- On a graph of a transverse wave, the distance between two successive peaks is 0.5 m and the wave travels at 4 m s⁻¹. What is the frequency?
- A longitudinal sound wave in air has a wavelength of 0.68 m. If the speed of sound is 340 m s⁻¹, calculate the frequency.
- Given the wave equation \$y(x,t)=0.02\sin(4\pi x-6\pi t)\$, find the amplitude, wavelength, and period.
7️⃣ Analogy Corner 🌟
Think of a transverse wave like a seesaw – the up and down motion is perpendicular to the line of the seesaw. A longitudinal wave is like a crowd wave at a stadium – people push and pull in the same direction as the wave moves.