HKDSE Physics Core
Chapter 4: Wave Phenomena | 波動現象
Billy Sir’s Smart Notes: Master Ripple Tank, Reflection, Refraction, Diffraction, Interference, and Stationary Waves.
由中大物理系碩士 Billy Sir 編寫，助你極速掌握水波槽、反射、折射、繞射、干涉及駐波。
1. Ripple Tank Illustration | 水波槽示範
A ripple tank is used to study the behavior of water waves in a laboratory. A light source above the tank projects the wave pattern onto a screen below. 水波槽用於在實驗室中研究水波的行為。槽上方的光源將波的圖案投影到下方的屏幕上。
- Bright fringes (亮紋): Act like convex lenses, formed by wave crests (波峰).
- Dark fringes (暗紋): Act like concave lenses, formed by wave troughs (波谷).
- The distance between two consecutive bright fringes equals one wavelength (\( \lambda \)). (兩條相鄰亮紋的距離等於一個波長)
2. Wave Reflection | 波的反射
When a wave hits a barrier, it bounces back. This is called reflection. 當波遇到障礙物時會反彈，這稱為反射。
🪞 Law of Reflection | 反射定律
Key Properties after Reflection:
- Speed (\( v \)): Unchanged (不變)
- Frequency (\( f \)): Unchanged (不變)
- Wavelength (\( \lambda \)): Unchanged (不變)
3. Wave Refraction | 波的折射
Refraction occurs when a wave travels from one medium to another, changing its speed and usually its direction. For water waves, this happens when depth changes. 當波從一種介質進入另一種介質時，其速度和方向通常會改變，這稱為折射。對於水波，這發生在水深改變時。
| Property (特性) | Deep Water (深水區) | Shallow Water (淺水區) |
|---|---|---|
| Speed (\( v \)) | Faster (較快) | Slower (較慢) |
| Wavelength (\( \lambda \)) | Longer (較長) | Shorter (較短) |
| Frequency (\( f \)) | Always Unchanged (永遠不變) – determined by the source | |
| Direction (方向) | Bends away from normal (偏離法線) | Bends towards normal (偏向法線) |
4. Wave Diffraction | 波的繞射
Diffraction is the spreading out of waves when they pass through a gap or around an obstacle. 當波穿過縫隙或繞過障礙物時散開的現象稱為繞射。
📢 Factors Affecting the Degree of Diffraction | 影響繞射程度的因素
The degree of spreading (diffraction) depends on the relationship between the wavelength (\( \lambda \)) and the size of the gap or obstacle (\( a \)). (散開（繞射）的程度取決於波長與縫隙或障礙物大小的關係。)
- Gap Size (\( a \)): A narrower gap (smaller \( a \)) leads to a greater degree of diffraction. (縫隙越窄，繞射程度越大。)
- Wavelength (\( \lambda \)): A longer wavelength (larger \( \lambda \)) leads to a greater degree of diffraction. (波長越長，繞射程度越大。)
- When the gap size is roughly equal to the wavelength (\( a \approx \lambda \)), diffraction is highly noticeable. If the gap is much larger than the wavelength (\( a \gg \lambda \)), diffraction is negligible and the wave travels mostly straight.
- Speed, frequency, and wavelength remain unchanged during diffraction.
5. Wave Interference | 波的干涉
When two waves meet, they superpose (add up) to form a new wave. The basic requirement for an observable and stable interference pattern is that the waves must come from coherent sources. 當兩個波相遇時，它們會疊加形成一個新波。要形成可觀察且穩定的干涉圖案，基本要求是波必須來自相干波源。
🎯 Coherent Sources | 相干波源
Coherent sources are defined as sources that possess the following properties: (相干波源定義為具有以下特性的波源：)
- Same frequency (and thus the same wavelength). (相同的頻率和波長)
- Constant phase difference over time. (隨時間保持恆定的相位差)
- Similar amplitude (for complete destructive interference to occur). (相若的振幅，以確保能發生完全相消干涉)
| Type (類型) | Condition (條件) | Path Difference (\( \Delta d \)) | Result (結果) |
|---|---|---|---|
| Constructive Interference 相長干涉 |
Crest meets Crest OR Trough meets Trough (波峰遇波峰 或 波谷遇波谷) |
$$ n\lambda $$ (where \( n = 0, 1, 2… \)) |
Maximum amplitude (Antinode) (最大振幅，腹線) |
| Destructive Interference 相消干涉 |
Crest meets Trough (波峰遇波谷) |
$$ (n + 0.5)\lambda $$ (where \( n = 0, 1, 2… \)) |
Minimum/Zero amplitude (Node) (最小/零振幅，節線) |
6. Stationary (Standing) Waves | 駐波
A stationary wave is formed by the superposition of two identical waves (same frequency and amplitude) traveling in opposite directions. 駐波是由兩個頻率和振幅相同、但傳播方向相反的波疊加而成的。
🎸 Key Features of Stationary Waves | 駐波的特徵
- Nodes (節點): Points that remain permanently at rest (zero amplitude) due to complete destructive interference. (永遠保持靜止的點，振幅為零)
- Antinodes (腹點): Points that oscillate with maximum amplitude due to constructive interference. (以最大振幅振動的點)
- Distance between two consecutive nodes (or antinodes) = \( \frac{\lambda}{2} \). (兩個相鄰節點或腹點之間的距離為半個波長)
- Unlike progressive waves, stationary waves do not transfer energy from one place to another. (與行進波不同，駐波不會傳遞能量)
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