A wave is a disturbance that travels through a medium, carrying energy from one place to another without transporting matter. Think of a ripple spreading across a pond after you drop a stone 🌊, or the sound of a drum vibrating through the air 🎵.
| Quantity | Symbol | Definition | Units |
|---|---|---|---|
| Speed of the wave | \$v\$ | Distance travelled by the wave per unit time | m s⁻¹ |
| Frequency | \$f\$ | Number of complete cycles per second | Hz (s⁻¹) |
| Wavelength | \$\lambda\$ | Distance between two successive points in phase (e.g., crest to crest) | m |
Let’s imagine a wave traveling along a string. In one second, the wave will have moved a certain distance – that’s the speed \$v\$. During that same second, the wave will have completed \$f\$ full cycles. Each cycle covers a distance equal to one wavelength \$\lambda\$. Therefore:
In block form, the wave equation is:
\$v = f \lambda\$
Picture a train (the wave) moving along a straight track (the medium).
- The speed of the train is \$v\$.
- Each carriage represents one wavelength \$\lambda\$.
- The number of carriages that pass a fixed point every second is the frequency \$f\$.
If the train travels 100 m in one second and has 10 carriages, each carriage is 10 m long: \$v = 10 \times 10 = 100\$ m s⁻¹. That’s exactly the wave equation in action!
Answers:
1) \$\lambda = v/f = 340/170 = 2\$ m.
2) \$v = f\lambda = 0.5 \times 2 = 1\$ m s⁻¹.
3) Because \$v = f\lambda\$, if \$\lambda\$ is constant, increasing \$f\$ directly increases \$v\$.
- Speed \$v\$ tells us how fast a wave moves.
- Frequency \$f\$ counts how many cycles pass a point each second.
- Wavelength \$\lambda\$ measures the length of one cycle.
- The fundamental relationship is \$v = f \lambda\$, linking all three concepts.
Remember the train analogy: speed = (carriages per second) × (length of each carriage). That’s the heart of wave physics!