← 返回资讯屏轩教育 · 行业资讯

Constructive Interference | 相长干涉

2026-08-21 19:55 · 本文部分内容由AI辅助创作

📚 Constructive Interference | 相长干涉

In AQA A-level Physics, interference and superposition are central to wave behaviour. Constructive interference occurs when two or more coherent waves arrive at a point in phase, producing a resultant wave with an amplitude equal to the sum of the individual amplitudes. This article explains the conditions, experiments and applications you need to master for the examination.

在 AQA A-level 物理中，干涉与叠加是波动行为的核心内容。当两个或更多相干波以同相到达某一点时，就会发生相长干涉，产生振幅等于各波振幅之和的合波。本文讲解考试中必须掌握的条件、实验和应用。

1. The Principle of Superposition | 叠加原理

The principle of superposition states that when two or more waves meet at a point, the resultant displacement is the vector sum of the individual displacements. This principle applies to all linear waves, including mechanical waves on strings, sound waves and electromagnetic waves such as light.

叠加原理指出：当两个或更多波在某一点相遇时，合位移等于各波位移的矢量之和。该原理适用于所有线性波，包括弦上的机械波、声波以及光等电磁波。

If two crests meet, their displacements add together to make a larger crest. If a crest meets a trough of the same amplitude, they cancel out. Constructive interference is the special case where the individual displacements reinforce each other rather than cancel.

如果两个波峰相遇，它们的位移相加，形成更大的波峰。如果波峰遇到同振幅的波谷，则会相互抵消。相长干涉是一种特殊情况，此时各波的位移相互加强而不是抵消。

For two sinusoidal waves of the same frequency travelling in the same direction, the resultant amplitude is greatest when the phase difference between them is an integer multiple of 2π. This is the foundation of all constructive interference calculations.

对于两列同频率、同方向传播的正弦波，当它们之间的相位差为 2π 的整数倍时，合振幅最大。这是所有相长干涉计算的基础。

2. Coherence: The Key Requirement | 相干性：关键条件

For a stable interference pattern to be observed, the sources must be coherent. Coherent sources have a constant phase difference and the same frequency. In practice, a single laser or a monochromatic source with a single slit is used to produce coherent light.

要观察到稳定的干涉图样，波源必须相干。相干波源具有恒定的相位差和相同的频率。实际中通常使用单一激光器，或使用单色光源配合单缝来产生相干光。

A laser is an ideal coherent source because it emits light of a single wavelength with all waves in step. In a laboratory, a sodium lamp or a filtered white light source can be made sufficiently coherent by passing the light through a narrow single slit before it reaches the double slit.

激光器是理想的相干光源，因为它发出单一波长的光且所有波都同相。在实验室中，钠灯或加滤光片的白光光源可以先通过一个窄单缝，再到达双缝，以获得足够的相干性。

If two independent lamps are used, the phase difference changes randomly many times per second, so the eye cannot see a fixed interference pattern. Coherence is therefore essential for both constructive and destructive interference to be visible.

如果使用两个独立的灯泡，相位差每秒会随机变化很多次，人眼无法看到固定的干涉图样。因此，相干性是观察到相长干涉和相消干涉的必要条件。

广告 / Sponsored

Cambridge International AS ALevel Physics Coursebook 正版剑桥国际AS ALevel考试物理教材带线上账号 英文原版
Cambridge International AS ALevel Physics Coursebook 正版剑桥国际AS ALevel考试物理教材带线上账号 英文原版
¥557.0
📱 去京东购买
京东精选

3. Phase Difference and Path Difference | 相位差与路程差

Phase difference describes how far one wave is ahead or behind another in its cycle. It is measured in radians or degrees. Path difference is the difference in distance travelled by two waves from their sources to a common point.

相位差描述一个波在周期中领先或落后另一个波的程度，以弧度或度为单位。路程差是两个波从各自波源传播到同一公共点的距离之差。

The phase difference is related to the path difference by the wavelength. If the path difference is one whole wavelength, the phase difference is 2π radians (360°), so the waves arrive in phase. If the path difference is half a wavelength, the phase difference is π radians (180°), so the waves arrive in anti-phase.

相位差通过波长与路程差相关联。如果路程差是一个完整的波长，相位差为 2π 弧度（360°），因此两列波同相到达。如果路程差是半个波长，相位差为 π 弧度（180°），因此两列波反相到达。

phase difference = (2π / λ) × path difference

This relationship is essential when you need to convert between path difference and phase difference in exam questions. Always express the path difference in metres and the wavelength in metres before using this equation.

在考试题目中需要在路程差和相位差之间转换时，这个关系式非常重要。使用该方程前，务必将路程差和波长都以米为单位表示。

4. Constructive Interference Condition | 相长干涉的条件

Constructive interference occurs when the waves arrive in phase. The condition can be stated using path difference or phase difference. For two coherent sources, constructive interference happens when the path difference is an integer multiple of the wavelength.

当波同相到达时会发生相长干涉。该条件可以用路程差或相位差表述。对于两个相干波源，当路程差为波长的整数倍时，就会发生相长干涉。