1. Overview
Waves are oscillations that transfer energy from one place to another without transferring matter. Understanding wave properties is essential because it explains how we see (light waves), how we hear (sound waves), and how modern communication technology functions.
Key Definitions
- Amplitude: The maximum displacement of a point on a wave from its undisturbed (rest) position.
- Wavelength ($\lambda$): The distance between a point on one wave and the equivalent point on the next adjacent wave (e.g., crest to crest).
- Frequency ($f$): The number of waves passing a point per second (measured in Hertz, Hz).
- Period ($T$): The time taken for one complete wave to pass a point.
- Wavefront: A line representing all the points on a wave that are in the same phase (e.g., a line connecting all the crests).
- Crest (Peak): The highest point of a transverse wave.
- Trough: The lowest point of a transverse wave.
- Wave Speed ($v$): The speed at which energy is transferred through a medium.
Core Content
Wave Motion and Energy Transfer
Waves transfer energy without transferring matter.
- In a rope: If you shake one end, the energy travels to the other end, but the rope fibers only move up and down.
- In water: A buoy or a leaf on the surface will bob up and down as a wave passes, but it will not move forward with the wave.
Transverse vs. Longitudinal Waves
Transverse Waves:
- Vibrations are at right angles (90°) to the direction of energy travel.
- Examples: Light (all electromagnetic radiation), water waves, and seismic S-waves.
- A wave showing peaks and troughs with an arrow pointing right for 'Direction of Travel' and a vertical double-headed arrow for 'Direction of Vibration'
Longitudinal Waves:
- Vibrations are parallel to the direction of energy travel.
- Consist of compressions (points bunched together) and rarefactions (points stretched apart).
- Examples: Sound waves and seismic P-waves.
- A spring/slinky showing compressed coils and stretched coils
Describing Waves
- Wave Speed ($v$): Calculated by multiplying frequency by wavelength.
- Calculation Example:
- Question: A wave has a frequency of 10 Hz and a wavelength of 2 m. Calculate the speed.
- Solution: $v = f \times \lambda = 10 \times 2 = 20 \text{ m/s}$.
Wave Behaviors & The Ripple Tank
A ripple tank uses a vibrating bar to create water waves.
- Reflection: Waves hit a flat (plane) barrier and bounce off. The angle of incidence equals the angle of reflection.
- Refraction: Waves change speed and direction when crossing a boundary. In a ripple tank, this is done by changing the depth.
- Deep water = Faster waves = Longer wavelength.
- Shallow water = Slower waves = Shorter wavelength.
- Note: The frequency never changes during refraction.
- Diffraction: The spreading out of waves as they pass through a gap or around an edge.
Extended Content (Extended Only)
Factors Affecting Diffraction
Diffraction is most noticeable when the size of the gap is similar to the wavelength of the wave.
Gap Size:
- If the gap is much wider than the wavelength, the waves pass through with very little spreading (mostly just at the edges).
- If the gap is narrow (close to the size of the wavelength), the waves spread out in wide semi-circles.
- Two panels; one shows waves passing through a wide gap with slight curving at edges; the second shows waves passing through a narrow gap becoming circular
Wavelength:
- Longer wavelengths diffract (spread) more than shorter wavelengths when passing through the same gap or around an edge.
- This explains why you can hear someone talking around a corner (long sound waves diffract) but you cannot see them (short light waves do not diffract significantly).
Key Equations
| Equation | Symbols | Units |
|---|---|---|
| $v = f \lambda$ | $v$ = speed, $f$ = frequency, $\lambda$ = wavelength | $v$ (m/s), $f$ (Hz), $\lambda$ (m) |
| $f = 1 / T$ | $f$ = frequency, $T$ = period | $f$ (Hz), $T$ (s) |
Common Mistakes to Avoid
- ❌ Wrong: Measuring amplitude from the trough to the crest.
- ✅ Right: Amplitude is measured from the center (equilibrium) line to the crest. If the total vertical height is 6 cm, the amplitude is 3 cm.
- ❌ Wrong: Thinking the frequency changes when waves enter shallow water or a new medium.
- ✅ Right: Frequency stays constant. Only speed and wavelength change during refraction.
- ❌ Wrong: Assuming a longer wave must be taller.
- ✅ Right: Wavelength (length) and Amplitude (height) are independent properties. A long wave can have a small amplitude.
- ❌ Wrong: Calculating wave speed from a displacement-distance graph alone.
- ✅ Right: You can find wavelength from a distance graph, but you need frequency or a displacement-time graph to find the speed.
Exam Tips
- Check your units: Ensure wavelength is in meters (m) and not centimeters (cm) before using the $v = f \lambda$ equation.
- The "Frequency Constant" Rule: In any question about refraction (waves changing speed), always remember that the frequency is determined by the source and does not change.
- Diffraction Drawing: When drawing diffracted waves, ensure the wavelength stays the same before and after the gap. Only the shape changes (it becomes circular), not the distance between the lines.