AS AQA Physics Unit 2 Revision Guide: Waves, Mechanics and Materials | AQA AS 物理第二单元复习指南：波、力学与材料

📚 AS AQA Physics Unit 2 Revision Guide: Waves, Mechanics and Materials | AQA AS 物理第二单元复习指南：波、力学与材料

The January 2019 AQA AS Physics Unit 2 insert provides a valuable window into how the exam board tests your understanding of waves, mechanics and materials. This revision guide breaks down the core concepts you need to master, with worked examples and examiner-style tips drawn from the question stems and data tables typical of this paper.

2019年1月AQA AS物理第二单元试卷的插页材料为我们提供了一个宝贵的窗口，展示考试局如何测试你对波、力学和材料等核心概念的理解。本复习指南基于该试卷典型的问题情境和数据表格，系统地拆解你需要掌握的核心知识点，并提供例题和考官风格的答题技巧。

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1. Progressive Waves and Wave Properties | 行波与波动性质

A progressive wave transfers energy from one point to another without transferring matter. The key quantities are wavelength (λ), frequency (f), and wave speed (v), related by v = fλ. For a transverse wave, particles oscillate perpendicular to the direction of energy transfer; for a longitudinal wave, they oscillate parallel to it.

行波将能量从一点传递到另一点，但不传递物质。关键物理量包括波长（λ）、频率（f）和波速（v），它们之间的关系为 v = fλ。对于横波，质点振动方向垂直于能量传播方向；对于纵波，质点振动方向平行于能量传播方向。

v = fλ

When reading data from an insert about a wave on a string or a sound wave, always check the units. A typical exam question might give you the distance between consecutive compressions in a longitudinal wave — this equals one wavelength directly.

当从试卷插页中读取关于绳波或声波的数据时，务必检查单位。典型的考题可能给出纵波中相邻密部之间的距离——这直接等于一个波长。

• Displacement (s): distance from equilibrium position, measured in metres.

  位移（s）：偏离平衡位置的距离，单位为米。

• Amplitude (A): maximum displacement from equilibrium.

  振幅（A）：偏离平衡位置的最大位移。

• Period (T): time for one complete oscillation, T = 1/f.

  周期（T）：完成一次完整振动所需的时间，T = 1/f。

• Phase difference: measured in radians or degrees, showing how much one point leads or lags another.

  相位差：以弧度或度为单位，表示某点超前或滞后于另一点的程度。

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2. Superposition Principle | 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 is the foundation of interference and stationary waves.

叠加原理指出，当两列或多列波在空间某点相遇时，合位移等于各列波单独在该点产生的位移的矢量和。这是干涉和驻波的基础。

The insert for January 2019 often includes a diagram of two pulses approaching each other. You must be able to sketch the resultant wave shape at a given time, and then predict the shape after the pulses have passed through each other — they pass through unchanged.

2019年1月的试卷插页通常包含两列脉冲相互靠近的示意图。你必须能够画出在给定时刻合成波的形状，并预测脉冲相互穿过之后的形状——它们穿过彼此后保持不变。

Resultant displacement = s₁ + s₂

For waves that are in phase, constructive interference occurs (amplitudes add). For waves exactly out of phase (phase difference = π radians or 180°), destructive interference occurs (amplitudes cancel).

对于同相波，发生相长干涉（振幅相加）。对于恰好反相的波（相位差 = π 弧度或 180°），发生相消干涉（振幅相消）。

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3. Stationary (Standing) Waves | 驻波

A stationary wave forms when two progressive waves of the same frequency and amplitude travel in opposite directions and superpose. The insert may show a vibrating string or an air column in a resonance tube. Nodes are points of zero displacement; antinodes are points of maximum displacement.

驻波由两列频率和振幅相同、传播方向相反的波叠加而成。插页可能显示振动的弦或共鸣管中的空气柱。波节是位移始终为零的点；波腹是位移最大的点。

Key equations for stationary waves on a string fixed at both ends:

两端固定的弦上形成驻波的关键公式：

f₁ = (1/2L)√(T/μ) for the fundamental frequency

基频 f₁ = (1/2L)√(T/μ)

• L is the length of the string, T is the tension, μ is the mass per unit length.

  L 为弦长，T 为张力，μ 为单位长度的质量（线密度）。

• Harmonics: fₙ = nf₁, where n = 1, 2, 3…

  谐波：fₙ = nf₁，其中 n = 1, 2, 3…

• For a pipe open at both ends, antinodes form at both ends; for a pipe closed at one end, a node forms at the closed end.

  对于两端开口的管，两端均形成波腹；对于一端封闭的管，封闭端形成波节。

The distance between adjacent nodes (or adjacent antinodes) is always λ/2. This is a frequently tested fact in data-based questions.

相邻波节（或相邻波腹）之间的距离始终为 λ/2。这是基于数据的问题中经常考查的知识点。

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4. Interference and Young’s Double Slit | 干涉与杨氏双缝实验

For coherent sources — waves with a constant phase difference — interference patterns are stable. The Jan 19 insert may ask you to identify conditions for clear interference fringes: coherent sources, similar amplitude, and overlapping waves.

对于相干波源——相位差恒定的波——干涉图样是稳定的。2019年1月的插页可能要求你识别产生清晰干涉条纹的条件：相干波源、振幅相近、波发生重叠。

w = λD / a

For Young’s double slit, w is the fringe spacing, λ is the wavelength of light, D is the distance from the slits to the screen, and a is the slit separation. If the insert provides data such as D = 2.5 m, a = 0.5 mm and w = 3.0 mm, you can solve for λ.

在杨氏双缝实验中，w 为条纹间距，λ 为光的波长，D 为双缝到屏幕的距离，a 为双缝间距。如果插页提供的数据为 D = 2.5 m，a = 0.5 mm，w = 3.0 mm，你可以求解 λ。

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5. Diffraction | 衍射

Diffraction is the spreading of waves when they pass through a gap or around an obstacle. The amount of diffraction depends on the wavelength relative to the size of the gap. When the gap width is comparable to the wavelength, significant spreading occurs.

衍射是波通过狭缝或绕过障碍物时发生的展宽现象。衍射程度取决于波长与狭缝尺寸的相对关系。当狭缝宽度与波长相当时，会发生显著的展宽。

For a single slit, the diffraction pattern consists of a central maximum (twice the width of other maxima) with weaker secondary maxima on either side. The insert might show the pattern and ask you to explain the minima using path difference: a minimum occurs when waves from across the slit cancel in pairs.

对于单缝衍射，衍射图样由一个中央明纹（宽度是其他明纹的两倍）和两侧较弱的次级明纹组成。插页可能展示该图样，并要求你利用光程差解释暗纹：当来自缝上不同位置的波成对相消时，出现暗纹。

• Diffraction is most noticeable when gap width ≈ wavelength.

  当缝宽 ≈ 波长时，衍射现象最明显。

• For all waves, longer wavelengths diffract more.

  对所有波而言，波长越长，衍射越明显。

• In a diffraction grating, nλ = d sinθ, where d is the grating spacing.

  在衍射光栅中，nλ = d sinθ，其中 d 为光栅间距。

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6. Refraction and Refractive Index | 折射与折射率

When a wave passes from one medium to another, its speed and wavelength change, causing it to change direction. The refractive index n is defined as n = c/v, where c is the speed of light in a vacuum and v is the speed in the medium.

当波从一种介质进入另一种介质时，其速度和波长发生变化，从而导致传播方向改变。折射率 n 的定义为 n = c/v，其中 c 是真空中的光速，v 是介质中的光速。

n₁ sinθ₁ = n₂ sinθ₂ (Snell’s law)

n₁ sinθ₁ = n₂ sinθ₂（斯涅耳定律）

Total internal reflection occurs when the angle of incidence exceeds the critical angle, where sinθ꜀ = 1/n (from a denser to a rarer medium). The Jan 19 insert might include data on optical fibres — cladding with a lower refractive index ensures total internal reflection along the fibre.

当入射角超过临界角时，发生全内反射，临界角满足 sinθ꜀ = 1/n（光线从光密介质射向光疏介质）。2019年1月的插页可能包含光学纤维的数据——包层的折射率更低，确保光线沿纤维发生全内反射。

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7. Kinematics and Motion Graphs | 运动学与运动图像

This section focuses on describing motion using equations and graphs. The insert may provide displacement-time or velocity-time data from an experiment. You must be able to calculate gradients and areas under graphs to find velocities and displacements.

本部分侧重于用方程和图像描述运动。插页可能提供来自实验的位移-时间或速度-时间数据。你必须能够计算斜率以及曲线下的面积，从而求出速度和位移。

The constant acceleration (SUVAT) equations are essential:

匀加速运动（SUVAT）方程至关重要：

v = u + at, s = ut + ½at², v² = u² + 2as

• Velocity-time graph: gradient = acceleration, area under graph = displacement.

  速度-时间图像：斜率 = 加速度，曲线下面积 = 位移。

• Displacement-time graph: gradient = velocity.

  位移-时间图像：斜率 = 速度。

• At maximum height in projectile motion, velocity is momentarily zero.

  在抛体运动的最高点，速度瞬时为零。

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8. Newton’s Laws and Forces | 牛顿定律与力

Newton’s three laws are the cornerstone of mechanics. The insert is likely to present a scenario such as a block on a rough surface or a trolley accelerated by a falling mass. You must identify all forces and apply F = ma.

牛顿三大定律是力学的基石。插页可能呈现一个情景，例如粗糙表面上的物块或被下落重物加速的小车。你必须识别所有力并应用 F = ma。

F = ma, weight W = mg

• First law: a body remains at rest or moves at constant velocity unless acted on by a resultant force.

  第一定律：物体在不受合外力作用时保持静止或做匀速直线运动。

• Second law: resultant force equals rate of change of momentum, or F = ma for constant mass.

  第二定律：合外力等于动量变化率；对于质量恒定的物体，可写为 F = ma。

• Third law: forces always occur in equal and opposite pairs acting on different bodies.

  第三定律：力总是成对出现，大小相等、方向相反，作用在不同物体上。

When drawing force diagrams from insert data, remember that the normal contact force is perpendicular to the surface, friction opposes relative motion, and tension acts along a string away from the object.

根据插页数据画受力图时，注意法向接触力垂直于表面，摩擦力阻碍相对运动，张力沿绳子方向并对物体施加拉力。

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9. Work, Energy and Power | 功、能量与功率

Work done is the product of force and distance moved in the direction of the force. Energy is the capacity to do work, and power is the rate of doing work. The insert might contain efficiency data for a machine or information about energy transfers in a bouncing ball experiment.

功是力与物体在力的方向上移动距离的乘积。能量是做功的能力，功率是做功的速率。插页可能包含某台机器的效率数据或弹跳球实验中的能量转化信息。

W = Fs, KE = ½mv², GPE = mgh, P = W/t

• Kinetic energy: energy due to motion.

  动能：物体由于运动而具有的能量。

• Gravitational potential energy: energy due to height in a gravitational field.

  重力势能：物体在重力场中由于高度而具有的能量。

• Conservation of energy: total energy in a closed system remains constant.

  能量守恒：封闭系统中总能量保持不变。

• Efficiency = useful output energy ÷ total input energy (× 100%).

  效率 = 有用输出能量 ÷ 总输入能量（× 100%）。

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10. Momentum and Collisions | 动量与碰撞

Momentum is the product of mass and velocity. In any closed system, total momentum is conserved. The Jan 19 insert might give data from a collision experiment with two trolleys of known masses and velocities before and after impact.

动量是质量与速度的乘积。在任何封闭系统中，总动量守恒。2019年1月的插页可能提供碰撞实验数据，涉及两辆质量与碰撞前后速度已知的小车。

p = mv, momentum before = momentum after

In an elastic collision, both momentum and kinetic energy are conserved. In an inelastic collision, kinetic energy is not conserved — some is converted to heat, sound or deformation energy. A perfectly inelastic collision is one where the objects stick together.

在弹性碰撞中，动量和动能均守恒。在非弹性碰撞中，动能不守恒——部分动能转化为热能、声能或形变能。完全非弹性碰撞是指碰撞后物体粘在一起运动的碰撞。

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11. Materials: Hooke’s Law and Elasticity | 材料：胡克定律与弹性

Hooke’s law states that the extension of a spring is directly proportional to the applied force, provided the limit of proportionality is not exceeded. The insert is very likely to include a force-extension table for you to analyse.

胡克定律指出，在比例极限之内，弹簧的伸长量与所受外力成正比。插页很可能包含一组力-伸长数据表供你分析。

F = kx

• k is the spring constant (force per unit extension), measured in N m⁻¹.

  k 为劲度系数（单位伸长所需的力），单位为 N m⁻¹。

• The gradient of a force-extension graph gives the spring constant.

  力-伸长图像的斜率给出劲度系数。

• Elastic deformation is reversible; plastic deformation is permanent.

  弹性形变是可逆的；塑性形变是永久性的。

• Elastic strain energy E = ½kx² = area under force-extension graph.

  弹性应变能 E = ½kx² = 力-伸长图像下的面积。

A common insert question shows two springs in series or parallel. In series, spring constants combine as 1/k_total = 1/k₁ + 1/k₂; in parallel, k_total = k₁ + k₂. Practice deriving these from the definition of stiffness.

一个常见的插页问题展示两个弹簧串联或并联。串联时，劲度系数满足 1/k_total = 1/k₁ + 1/k₂；并联时，k_total = k₁ + k₂。请练习从劲度的定义出发推导这些关系。

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12. Stress, Strain and Young Modulus | 应力、应变与杨氏模量

Stress is the force per unit cross-sectional area and strain is the fractional change in length. The Young modulus is the ratio of stress to strain and is a measure of the stiffness of a material. Data from the insert, such as a wire’s original length and diameter, is used in these calculations.

应力是单位横截面积上的力，应变是长度变化量与原始长度之比。杨氏模量是应力与应变的比值，是衡量材料刚度的物理量。插页中的数据，如金属丝的原始长度和直径，可用于这些计算。

stress = F/A, strain = ΔL/L, E = stress / strain = FL / (AΔL)

Typical values: steel has E ≈ 2.1 × 10¹¹ Pa, while rubber has a much lower value. The insert may give you experimental data to plot a stress-strain graph; the gradient of the initial straight-line region equals the Young modulus.

典型数值：钢的杨氏模量约为 2.1 × 10¹¹ Pa，而橡胶的值要低得多。插页可能提供实验数据供你绘制应力-应变图；初始直线段的斜率等于杨氏模量。

• The ultimate tensile stress is the maximum stress a material can withstand without breaking.

  极限抗拉强度是材料在断裂前所能承受的最大应力。

• Brittle materials (e.g. glass) show little plastic deformation before breaking; ductile materials (e.g. copper) show significant plastic deformation.

  脆性材料（如玻璃）在断裂前几乎没有塑性形变；延性材料（如铜）在断裂前有明显塑性形变。

• Units: stress in Pa (N m⁻²) or MPa, strain has no units, E in Pa.

  单位：应力为 Pa（N m⁻²）或 MPa，应变为无量纲量，E 的单位为 Pa。

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