15.3 Content
15.3.1 What is a Wave?
A wave is a disturbance that transfers energy through a medium (or through space) without transferring matter. The particles of the medium oscillate about their equilibrium positions while the wave pattern moves through.
Waves transfer energy without transferring matter. The medium oscillates locally; the disturbance propagates.
15.3.2 Wave Vocabulary
| Property | Symbol | Definition | Unit |
|---|---|---|---|
| Amplitude | \(A\) | Maximum displacement from equilibrium | m |
| Wavelength | \(\lambda\) | Distance between repeating points | m |
| Period | \(T\) | Time for one complete cycle | s |
| Frequency | \(f\) | Number of cycles per second | Hz |
| Wave speed | \(v\) | Speed of wave propagation | m/s |
15.3.3 Interactive: Transverse Wave Anatomy
Explore the properties of a transverse wave:
Key features to observe:
- Crest: The highest point of the wave
- Trough: The lowest point of the wave
- Amplitude: Distance from equilibrium to crest (or trough)
- Wavelength: Distance from one crest to the next
15.3.4 Transverse and Longitudinal Waves
Transverse waves oscillate perpendicular to the direction of travel:
- Examples: Light, water surface waves, waves on a string
- Particles move up-and-down while wave moves horizontally
Longitudinal waves oscillate parallel to the direction of travel:
- Examples: Sound, seismic P-waves, spring compression waves
- Particles move back-and-forth along the wave direction
15.3.5 Interactive: Wave Types Comparison
Compare transverse oscillation:
15.3.6 The Wave Equation
Wave speed, frequency, and wavelength are related by:
\[v = f\lambda\]
This equation applies to all waves—mechanical, electromagnetic, or otherwise.
Since period and frequency are reciprocals:
\[T = \frac{1}{f} \quad \text{and} \quad f = \frac{1}{T}\]
We can also write: \[v = \frac{\lambda}{T}\]
Given any two of \(v\), \(f\), \(\lambda\), you can find the third: - \(v = f\lambda\) - \(f = v/\lambda\) - \(\lambda = v/f\)
15.3.7 Wave Speed in Different Media
Wave speed depends on the medium, not on frequency or amplitude.
| Wave Type | Medium Factor | Speed depends on |
|---|---|---|
| Waves on string | Tension, linear density | \(v = \sqrt{T/\mu}\) |
| Sound | Temperature, medium type | ~340 m/s in air at 20°C |
| Light | Refractive index | \(c/n\) where \(c = 3 \times 10^8\) m/s |
15.3.8 Interactive: Different Frequencies, Same Speed
Two waves with different frequencies travel at the same speed:
Higher frequency = shorter wavelength (for the same wave speed).