📚 OxfordAQA International AS Physics: Oscillations and Waves – Concept Review | 牛津AQA国际AS物理：振动与波 – 概念解析
Oscillations and waves form a cornerstone of the OxfordAQA International AS Physics syllabus, linking the motion of individual particles to the transfer of energy without net matter transport. This article unpacks the key concepts you must master, from simple harmonic motion to standing waves, preparing you effectively for topic tests and the final exam.
振动和波是牛津AQA国际AS物理课程的核心内容，将单个粒子的运动与能量的传递（而无净物质输运）联系起来。本文梳理你必须掌握的关键概念，从简谐运动到驻波，帮助你高效备考单元测验与最终考试。
1. Simple Harmonic Motion (SHM) | 简谐运动（SHM）
m the equilibrium position and always directed towards that equilibrium. Mathematically, a ∝ –x, or a = –ω²x, where ω is the angular frequency.
简谐运动被定义为加速度与偏离平衡位置的位移成正比，且始终指向平衡位置的振荡运动。数学上表示为 a ∝ –x，或 a = –ω²x，其中 ω 是角频率。
An object moving with SHM traces out a sinusoidal pattern in time. The motion is isochronous: the period T is independent of the amplitude for a given system, provided the restoring force obeys Hooke's law and damping is negligible.
做简谐运动的物体在时间上描绘出正弦图样。这种运动是等时的：对于给定系统，只要回复力服从胡克定律且阻尼可忽略，周期 T 与振幅无关。
2. Kinematics of SHM | 简谐运动的运动学
maximum displacement from equilibrium. The velocity v is the gradient of the displacement–time graph: v = ±ω√A² – x² or v = Aω cos(ωt) when x = A sin(ωt).
简谐运动质点的位移 x 可写成 x = A sin(ωt) 或 x = A cos(ωt)，取决于初始条件。A 是振幅，即离开平衡位置的最大位移。速度 v 是位移–时间图的斜率：v = ±ω√A² – x²，当 x = A sin(ωt) 时 v = Aω cos(ωt)。
The acceleration a is obtained by differentiating again, giving a = –ω²x. The maximum speed occurs as the particle passes through equilibrium (vmax = ωA), and the maximum acceleration occurs at the extreme positions (amax = ω²A).
加速度 a 再次求导可得 a = –ω²x。粒子经过平衡位置时速率最大 (vmax = ωA)，在极端位置时加速度最大 (amax = ω²A)。
3. Dynamics of SHM: The Restoring Force | 简谐运动的动力学：回复力
For a mechanical oscillator, the condition a = –ω²x implies a net restoring force F = – nstant) and a simple pendulum for small angles (k = mg/L, where L is the pendulum length).
对于机械振子，条件 a = –ω²x 意味着净回复力 F = –kx，其中 k 是劲度系数。例子包括弹簧上的物块（k 为弹簧劲度系数）和摆角很小的单摆（k = mg/L，L 为摆长）。
From F = –kx and Newton’s second law, the period of a mass–spring system is T = 2π√m/k, where m is the mass. For a simple pendulum, T = 2π√L/g. These expressions show that frequency is determined by the physical properties of the oscillator, not by the amplitude.
由 F = –kx 和牛顿第二定律，弹簧振子的周期为 T = 2π√m/k，其中 m 是质量。单摆的周期为 T = 2π√L/g。这些表达式表明频率由振子本身的物理性质决定，与振幅无关。
4. Energy Transformations in SHM | 简谐运动中的能量转换
In undamped SHM, total mechanical energy remains constant. Kinetic energy Ek = ½ mv² and potential energy Ep = ½ kx² interchange continuously. At equilibrium, Ek is maximum and Ep is zero; at the extremes, Ek = 0 and Ep = ½ kA².
在无阻尼简谐运动中，总机械能保持不变。动能 Ek = ½ mv² 与势能 Ep = ½ kx² 不断相互转换。在平衡位置，Ek 最大而 Ep 为零；在极端位置，Ek = 0，Ep = ½ kA²。
The total energy Etotal t displacement or time show how the sum remains flat while kinetic and potential components oscillate at twice the frequency of the displacement.
总能量 Etotal = ½ kA² = ½ mω²A²。能量随位移或时间的变化图显示总和保持恒定，而动、势两部分以两倍于位移的频率振荡。
5. Damping and Resonance | 阻尼与共振
Damping removes energy from an oscillating system, usually due to resistive forces like air resistance or friction. Light damping gradually reduces amplitude; heavy damping causes the system to return to equilibrium without oscillating; critical damping brings it to rest in the shortest possible time.
阻尼会从振动系统中移除能量，通常由空气阻力或摩擦等耗散力造成。弱阻尼使振幅逐渐减小；强阻尼使系统不回摆直接回到平衡位置；临界阻尼使系统在最短时间内静止。
When a system is driven by a periodic external force at a frequency close to its natural frequency, resonance occurs. The amplitude of oscillation becomes very large. Resonance can be useful (e.g., in a microwave oven) or destructive (e.g., bridges collapsing), so engineers often design damping into structures to limit resonant amplitudes.
当系统受到频率接近其固有频率的周期性外力驱动时，就会发生共振。振幅变得非常大。共振可能有益（如微波炉），也可能有害（如桥梁坍塌），因此工程师通常在设计时引入阻尼以限制共振振幅。
6. Wave Characteristics and the Wave Equation | 波的特征与波动方程
est), wavelength λ (distance between two consecutive points in phase), period T (time for one complete oscillation at a point), and frequency f (number of oscillations per second, f = 1/T).
波将能量从一点传递到另一点，而没有物质的整体输运。关键描述量包括振幅 A（离开平衡位置的最大位移）、波长 λ（两个相邻同相位点间的距离）、周期 T（某一点完成一次完整振动所需的时间）和频率 f（每秒振动次数，f = 1/T）。
s fundamental and applies to all types of wave. For mechanical waves, speed depends on the properties of the medium (e.g., tension and linear density for a string).
v = f × λ
波速 v 由波动方程 v = f λ 给出。这一基本关系适用于所有类型的波。对机械波而言，波速取决于介质的性质（例如弦上的张力和线密度）。
7. Transverse and Longitudinal Waves; Polarisation | 横波与纵波；偏振
In a transverse wave, particle oscillations are perpendicular to the direction of energy propagation (e.g., light, waves on a string). In a longitudinal wave, oscillations are parallel to the propagation direction (e.g., sound waves in air).
在横波中，质点振动方向与能量传播方向垂直（例如光波、弦波）。在纵波中，振动方向与传播方向平行（例如空气中的声波）。
Only transverse waves can be polarised. Polarisation refers to the restriction of oscillations to a single plane. Unpolarised light vibrates in all planes perpendicular to the direction of travel; a polarising filter transmits only the component in one direction, reducing intensity according to Malus's law.
只有横波才能被偏振。偏振指的是将振动限制在单一平面内。非偏振光在与传播方向垂直的所有平面上振动；偏振片只让某一方向的分量透过，根据马吕斯定律光强会减小。
8. Superposition, Interference, and Coherence | 叠加、干涉与相干性
placements. This leads to interference effects: constructive interference when waves are in phase (path difference = nλ) and destructive interference when out of phase (path difference = (n + ½)λ).
叠加原理指出，当两个或多个波在一点相遇时，合位移是各个位移的矢量和。这导致干涉效应：当波同相时（程差 = nλ）发生相长干涉；当波反相时（程差 = (n + ½)λ）发生相消干涉。
For a stable interference pattern, the sources must be coherent – they must have the same frequency and a constant phase difference. Laser light is coherent; a double slit fed by a single slit provides near-coherent illumination from a white light source.
要获得稳定的干涉图样，波源必须是相干的——它们必须具有相同的频率和恒定的相位差。激光是相干光；由单缝照亮的双缝能为白光光源提供近似相干的照明。
9. Young’s Double Slit and Diffraction Gratings | 杨氏双缝与衍射光栅
Young’s double‑ tern of bright and dark fringes on a screen. The fringe spacing Δy is given by Δy = λD / d, where λ is the wavelength, D the slit‑to‑screen distance, and d the slit separation.
杨氏双缝实验证明了光的波动性。单色光通过两条靠近的狭缝，在屏幕上产生明暗相间的干涉条纹。条纹间距 Δy 由 Δy = λD / d 给出，其中 λ 为波长，D 为双缝到屏幕的距离，d 为狭缝间距。
he grating equation is d sinθ = nλ, where d is the grating spacing, θ the angle to the nth‑ mum, and n an integer. Gratings are used in spectroscopy to measure wavelengths precisely.
衍射光栅由大量等距狭缝构成，产生更细、更亮的极大值。光栅方程为 d sinθ = nλ，其中 d 为光栅间距，θ 为第 n 级明纹的衍射角，n 为整数。光栅在光谱学中被用来精确测量波长。
10. Stationary Waves on Strings and in Pipes | 弦和管内的驻波
A stationary (standing) wave forms when two identical waves travelling in opposite directions superpose. Unlike a progressive wave, nodes (points of zero displacement) and antinodes (points of maximum displacement) are fixed in space. Energy is not transferred along the medium – it is stored in the wave pattern.
当两列相同的波沿相反方向传播并叠加时，会形成驻波。与行波不同，驻波的波节（位移为零的点）和波腹（位移最大的点）在空间中固定不动。能量不沿介质传播，而是储存在波纹中。
at both ends, the fundamental frequency f₁ = v/(2L) arises when the length L equals a half‑ nd harmonic (first overtone) has f₂ = 2f₁ = v/L and one complete wavelength on the string.
对于两端固定的弦，当弦长 L 等于半波长时产生基频 f₁ = v/(2L)。泛音频率是基频的整数倍：二次谐波（第一泛音）f₂ = 2f₁ = v/L，弦上出现一个完整波长。
as a node at the closed end and an antinode at the open end, so the fundamental λ = 4L and f = v/(4L); only odd harmonics are present.
在管中可形成声驻波。开管两端均为波腹，因此基频波长 λ = 2L，f = v/(2L)。闭管在封闭端为波节、开口端为波腹，因此基频 λ = 4L，f = v/(4L)；只存在奇数倍谐波。
Published by TutorHao | Physics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图