General properties of waves
Waves transfer energy from one place to another without transferring matter.
This is the fundamental definition of a wave. When you see a cork bobbing up and down on water, the cork (matter) stays roughly in the same horizontal position while the energy travels across the surface.
We can illustrate this using:
- Mechanical waves: Vibrations in ropes, springs, or water require a medium (material) to travel through.
- Electromagnetic waves: These can travel through a vacuum (empty space).
Wave motion is the propagation of a disturbance. In a rope, this looks like a 'pulse' or a continuous vibration traveling along the length.
Key features of a wave:
- Crest (Peak): The highest point of the wave.
- Trough: The lowest point of the wave.
- Amplitude (a): The maximum displacement from the equilibrium (rest) position. It represents the energy carried by the wave.
- Wavelength (\lambda): The distance between two consecutive corresponding points on the wave (e.g., crest to crest or trough to trough).
- Frequency (f): The number of complete waves passing a point per second, measured in Hertz (Hz).
- Wave speed (v): How fast the energy travels, measured in meters per second (m/s).
- Wavefront: A line connecting points on adjacent waves that are in phase (e.g., all crests).
| Symbol/Unit |
|---|
| a (m) |
| \lambda (m) |
| f (Hz) |
v = f\lambda
Where:
- v = wave speed (m/s)
- f = frequency (Hz)
- \lambda = wavelength (m)
Why this works: Frequency (f) tells us how many waves pass per second. Wavelength (\lambda) is the length of one wave. Therefore, multiplying them gives the total distance covered by the wavefronts in one second (speed).
A wave has a frequency of 50 Hz and a wavelength of 2 m.
v = 50 \times 2 = 100 \text{ m/s}
Correct Understanding:
- Transverse waves: The direction of vibration is at right angles (perpendicular) to the direction of propagation. Examples: Electromagnetic radiation, water waves, seismic S-waves.
- Longitudinal waves: The direction of vibration is parallel to the direction of propagation. Examples: Sound waves, seismic P-waves.
Note: Sound is ALWAYS longitudinal. Water waves are a complex mix but are primarily modeled as transverse in this syllabus.
Examiner Acceptance: Examiners look for precise geometric language. You must state that the vibration is perpendicular (for transverse) or parallel (for longitudinal) to the direction of energy transfer/propagation.
Reasoning: Phrases like 'up and down' are too vague because they don't define the relationship to the wave's travel direction. 'Perpendicular' explicitly defines the 90-degree angle required by the definition of transverse waves.
Example Answer: "In a transverse wave, the particles vibrate perpendicular to the direction of wave propagation."
- In transverse waves, vibration is perpendicular to propagation; in longitudinal, it is parallel. 2. Transverse waves have crests and troughs; longitudinal waves have compressions and rarefactions.
1. Reflection:
- Waves bounce off a surface.
- The angle of incidence equals the angle of reflection.
2. Refraction:
- Waves change direction when they pass from one medium to another (or change depth in water).
- Cause: This happens because the speed of the wave changes. If the wave slows down, it bends towards the normal; if it speeds up, it bends away.
3. Diffraction:
- Waves spread out as they pass through a gap or around an obstacle.
- The amount of spreading depends on the relationship between the wavelength (\lambda) and the gap size (d).
Gap Diffraction (Supplement):
- Significant diffraction occurs when the gap size is approximately equal to the wavelength (d \approx \lambda).
- If the gap is much larger than the wavelength, little diffraction occurs.
- Wavelength effect: Longer wavelengths diffract more (spread out more) through a given gap.
Edge Diffraction (Supplement):
- Waves spread into the 'shadow region' behind an obstacle.
- Wavelength effect: Longer wavelengths bend around edges more effectively than shorter wavelengths.
A ripple tank uses a vibrating dipper to create water waves and a light source to project the wave pattern onto a screen below.
(a) Reflection:
- Setup: Plane waves hit a straight barrier (plane mirror).
- Observation: Waves bounce back. The reflected waves are parallel plane waves moving away from the barrier at the same angle as they approached.
(b) Refraction:
- Setup: A glass plate is placed in part of the tank to make the water shallower in that region.
- Observation: As waves enter the shallow region, their speed decreases. Consequently, the wavelength shortens, and the wavefronts bend towards the normal (change direction).
(c) Diffraction through a gap:
- Setup: Plane waves pass through a narrow slit.
- Observation: The straight wavefronts become semi-circular. The waves spread out into the region behind the barrier.
(d) Diffraction due to an edge (Supplement):
- Setup: Plane waves approach a straight barrier that blocks part of the wave path, leaving one open end (an edge).
- Observation: Waves spread out into the region behind the barrier (the shadow zone). The wavefronts become curved as they pass the edge, demonstrating that waves can bend around obstacles.
Key Comparison for Diffraction:
| Feature | Gap Diffraction | Edge Diffraction |
|---|---|---|
| Setup | Waves pass through an opening. | Waves pass by a barrier edge. |
| Visual Evidence | Semi-circular wavefronts centered on the gap. | Curved wavefronts spreading into the shadow region behind the barrier. |
| Wavelength Effect | Longer \lambda = more spreading. | Longer \lambda = more bending around the edge. |
Correct Understanding: Refraction is caused only by a change in speed. When a wave enters a new medium (or depth), its speed changes. Since v = f\lambda and frequency (f) remains constant (determined by the source), the wavelength (\lambda) must change to accommodate the new speed.
Examiner Acceptance: You must explicitly mention that the speed of the wave changes. Examiners accept 'speed decreases' as the primary reason. Mentioning that wavelength decreases is a secondary correct point, but speed is the root cause.
Reasoning: Frequency is constant in wave propagation across boundaries. Therefore, any change in direction (refraction) must be linked to the change in velocity vector, which is driven by the change in medium depth.
Example Answer: "The waves slow down as they enter the shallow water. This change in speed causes the wavefronts to bend."