波的性质

Q: 爱德思IGCSE物理的公式表中会给出波的相关公式吗？

不会，你必须熟记和两个公式，它们不会出现在考试提供的公式表中。

爱德思国际普通中等教育证书（IGCSE）物理· 3.1 - 3.9· 15 分钟阅读

1. 波的类型与核心性质★☆☆☆☆⏱ 3 min

🚫 计算器禁用

所有波都可以传递能量与信息，且不会发生净物质的转移。例如，当水波经过时，漂浮的软木塞只会上下浮动，不会被波带到岸边。

Transverse waves: Oscillations are perpendicular to the direction of energy transfer. Examples include all electromagnetic waves, water ripples, and waves on a stretched string.
Longitudinal waves: Oscillations are parallel to the direction of energy transfer, made of alternating compressions (high particle density) and rarefactions (low particle density). Examples include sound waves and seismic P-waves.

📐 例题

对光波和声波进行分类，并分别说明分类理由。

1
1. 光是一种电磁波：其电场与磁场的振荡方向与传播方向垂直，因此属于横波。
2
1. 声波通过空气粒子的振动传播，粒子振动方向与传播方向平行，存在压缩区和稀疏区，因此属于纵波。

2. 波的核心术语、单位与公式★★☆☆☆⏱ 4 min

✓ 计算器

📘 定义

波的核心物理量

A, \lambda, f, T

振幅（A）：相对于静止位置的最大位移，单位为米（m）。波长（ $λ$ ）：两个相邻同相位点之间的距离，单位为米（m）。频率（f）：每秒通过的波的数量，单位为赫兹（Hz）。周期（T）：一个完整波的传播时间，单位为秒（s）。波前：连接所有同相位振荡点的线。

例:

A 10 Hz sound wave has 10 complete waves passing a point every second, so its time period is 0.1 s.

本章节的两个公式不会出现在考试提供的公式表中，你必须熟练记忆：

v = f \times \lambda

f = \frac{1}{T}

📐 例题

某波的周期为0.02 s，计算其频率；若其波长为1.5 m，求该波的波速。

1
1. 使用公式 $f = 1/ T$ 计算频率：
2
$f = \frac{1}{0.02} = 50 \text{ Hz}$
3
1. 使用公式 $v = f λ$ 计算波速：
4
$v = 50 \times 1.5 = 75 \text{ m/s}$

3. 不同场景下的波的计算★★★☆☆⏱ 4 min

✓ 计算器

你需要在不同场景下应用波的相关公式，包括声波与电磁波。所有电磁波在真空中的传播速度均为 $3 \times 1 0^{8}$ m/s，所有电磁波相关计算题目都可以使用该数值。

📐 例题

某调频无线电波的频率为95 MHz，计算其波长。

1
1. 将频率转换为国际单位制单位（Hz）：
2
$95 \text{ MHz} = 95 \times 10^6 = 9.5 \times 10^7 \text{ Hz}$
3
1. 对公式 $v = f λ$ 变形，求解波长：
4
$\lambda = \frac{v}{f}$
5
1. 代入数值（电磁波的波速取 $v = 3 \times 1 0^{8}$ m/s）：
6
$\lambda = \frac{3 \times 10^8}{9.5 \times 10^7} \approx 3.16 \text{ m}$

✓ 快速检测

What is the period of a 200 Hz sound wave?
- A) 0.005 s
- B) 0.05 s
- C) 200 s
显示答案
A —
Use $T = 1/ f = 1/200 = 0.005$ s. Remember period is the inverse of frequency.
A sound wave travels at 340 m/s with a wavelength of 0.17 m. What is its frequency?
- A) 20 Hz
- B) 200 Hz
- C) 2000 Hz
显示答案
C —
Rearrange $v = f λ$ to $f = v / λ = 340/0.17 = 2000$ Hz.

4. 多普勒效应与波的核心行为★★☆☆☆⏱ 3 min

🚫 计算器禁用

📘 定义

多普勒效应

当波源相对于静止观察者运动时，观察者观测到的波的频率与波长发生变化的现象。波源自身发射的频率并未发生改变。

例:

An ambulance siren sounds higher pitched when approaching you, and lower pitched when driving away from you.

Source moving towards observer: Wavefronts bunch up in front of the source, observed wavelength is shorter, observed frequency is higher.
Source moving away from observer: Wavefronts stretch out behind the source, observed wavelength is longer, observed frequency is lower.

所有波（包括横波与纵波）都可以发生反射（在表面反弹）与折射（在两种不同介质间传播时改变速度与传播方向）。

📐 例题

请解释为什么静止的观察者听到救护车驶近时的警笛频率更高，而救护车驶离时的警笛频率更低。

1
1. 驶近阶段：救护车向观察者运动，因此声波的波前会在波源前方聚集。
2
1. 更短的观测波长会导致更高的观测频率，因此警笛的音调听起来更高。
3
1. 驶离阶段：波前在波源后方被拉伸，导致观测波长更长、观测频率更低，因此警笛的音调听起来更低。

5. 常见陷阱

错误做法:

Mixing up oscillation directions for transverse and longitudinal waves

原因:

This is a common 1-2 mark exam question, mixing the two loses easy marks

正确做法:

Remember transverse = perpendicular, longitudinal = parallel; use examples (EM = transverse, sound = longitudinal) to check your answer

错误做法:

Using non-SI units directly in wave calculations (e.g. kHz, cm)

原因:

Wave formulae only give correct answers when using SI units (Hz, m, m/s)

正确做法:

Convert all units to SI first: multiply kHz by 1000 to get Hz, multiply cm by 0.01 to get m

错误做法:

Stating that waves transfer matter as they travel

原因:

This is a common misconception tested in multiple choice questions

正确做法:

Recall that waves only transfer energy and information, with no net movement of matter particles

错误做法:

Using $f = T$ instead of $f = 1/ T$ for frequency calculations

原因:

The formula is not provided on the formula sheet, so misremembering it leads to wrong answers

正确做法:

Recall frequency is the number of waves per second, so divide 1 by the time for one wave (period) to get frequency

错误做法:

Claiming the Doppler effect changes the frequency emitted by the source

原因:

Examiners regularly test that only observed frequency changes, not source frequency

正确做法:

Clarify the source emits a constant frequency, only the observed frequency and wavelength change with relative movement

6. 速查表

Quantity	Symbol	Unit	Formula/Definition
Amplitude	A	m	Max displacement from rest position
Wavelength	$λ$	m	Distance between two adjacent in-phase points
Frequency	f	Hz	Number of waves per second; $f = 1/ T$
Time Period	T	s	Time for one complete wave; $T = 1/ f$
Wave Speed	v	m/s	$v = f \times λ$
Transverse Wave			Oscillations perpendicular to energy transfer
Longitudinal Wave			Oscillations parallel to energy transfer
Doppler (Approaching Source)			Observed f higher, $λ$ shorter
Doppler (Receding Source)			Observed f lower, $λ$ longer

7. 常见问题

爱德思IGCSE物理的公式表中会给出波的相关公式吗？

不会，你必须熟记 $v = f \times λ$ 和 $f = 1/ T$ 两个公式，它们不会出现在考试提供的公式表中。

本章节要求我计算多普勒频移的具体数值吗？

不需要，本章节仅要求对多普勒效应进行定性解释。红移的定量计算属于独立的天体物理学单元内容。

深入阅读

syllabus爱德思4PH1完整考纲请参考第3部分获取波单元的完整备考指导

下一步

Now that you have mastered core wave properties, you are ready to progress to the remaining sub-topics in the Edexcel IGCSE Physics waves unit. Next, you will learn about the full electromagnetic spectrum, including its ordering, common uses, and associated safety risks, as well as how EM wave properties apply to real-world technologies. Following that, you will explore detailed wave behaviours including the laws of reflection and refraction, ray diagrams, total internal reflection, and specific properties of sound waves. This foundational knowledge will also be critical when you later study astrophysics topics, including the Doppler red-shift evidence for the expansion of the universe. Make sure you memorize the two wave formulae and unit conversion rules, as they will appear frequently across all these subsequent topics.