HKDSE Physics Core
Chapter 3: Wave Propagation | 波動的傳播
Billy Sir’s Smart Notes: Master Wave Properties, Transverse vs Longitudinal Waves, and Wave Graphs.
由中大物理系碩士 Billy Sir 編寫，助你極速掌握波的特性、橫波與縱波及波動圖像。
1. Types of Waves | 波的種類
A wave transfers energy from one place to another without transferring matter. 波能把能量從一處傳遞到另一處，但不會傳遞物質。
| Wave Type (波的種類) | Particle Motion (粒子運動方向) | Key Features (主要特徵) | Examples (例子) |
|---|---|---|---|
| Transverse Wave 橫波 |
Perpendicular (\( \perp \)) to the direction of wave travel. 垂直於波的傳播方向。 |
Has Crests (highest points) and Troughs (lowest points). 具有波峰（最高點）和波谷（最低點）。 |
Water waves, Light (EM waves), waves on a string. 水波、光（電磁波）、繩波。 |
| Longitudinal Wave 縱波 |
Parallel (\( \parallel \)) to the direction of wave travel. 平行於波的傳播方向。 |
Has Compressions (particles close together) and Rarefactions (particles spread apart). 具有密部（粒子密集）和疏部（粒子稀疏）。 |
Sound waves, ultrasound, primary seismic waves (P-waves). 聲波、超聲波、地震P波。 |
2. Basic Wave Properties | 波的基本特性
| Property (特性) | Symbol & Unit | Definition (定義) |
|---|---|---|
| Amplitude 振幅 |
\( A \) (m) | The maximum displacement of a particle from its rest position. (粒子偏離平衡位置的最大位移) |
| Wavelength 波長 |
\( \lambda \) (m) | The distance between two consecutive points in phase (e.g., crest to crest). (兩個連續同相點之間的距離，如波峰到波峰) |
| Period 週期 |
\( T \) (s) | The time taken to produce one complete wave. (產生一個完整波所需的時間) |
| Frequency 頻率 |
\( f \) (Hz) | The number of complete waves produced per second. \( f = \frac{1}{T} \) (每秒產生的完整波的數目) |
🌊 The Wave Equation | 波動方程
The speed of a wave (\( v \)) is related to its frequency and wavelength: 波速與其頻率及波長有關：
$$ v = f \lambda $$
- \( v \) = Wave speed (m s\(^{-1}\)) (波速)
- \( f \) = Frequency (Hz) (頻率)
- \( \lambda \) = Wavelength (m) (波長)
3. Wave Graphs | 波動圖像
It is crucial to distinguish between the two types of wave graphs in exams! 在考試中，必須清楚分辨兩種波動圖像！
📸 1. Displacement-Distance Graph | 位移-距離圖像
This graph shows a “snapshot” of the whole wave at a specific instant in time. 這圖像顯示了波在某一瞬間的「快照」。
- x-axis: Distance from the source (\( x \)) (距離)
- y-axis: Displacement (\( d \)) (位移)
- What you can find:
- Amplitude (\( A \)): Maximum y-value.
- Wavelength (\( \lambda \)): Distance between two consecutive crests or troughs.
⏱️ 2. Displacement-Time Graph | 位移-時間圖像
This graph tracks the motion of a single particle over a period of time. 這圖像追蹤了單一粒子隨時間的運動。
- x-axis: Time (\( t \)) (時間)
- y-axis: Displacement (\( d \)) (位移)
- What you can find:
- Amplitude (\( A \)): Maximum y-value.
- Period (\( T \)): Time taken for one complete oscillation (e.g., peak to peak). Once you have \( T \), you can calculate \( f = \frac{1}{T} \).
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