Frequency and Angular Frequency | 频率与角频率

📚 Frequency and Angular Frequency | 频率与角频率

Frequency and angular frequency describe the same idea of repetition, but they count that repetition in different units. Frequency counts complete cycles per second, while angular frequency counts radians of phase per second. This distinction is essential in CIE A-Level Physics, especially in oscillations, waves, circular motion and alternating current.

频率和角频率描述的都是重复快慢，但计量单位不同。频率计算每秒完成的整周期数，角频率计算每秒扫过的相位弧度数。这个区别在 CIE A-Level 物理中至关重要，尤其是在振动、波动、圆周运动和交流电部分。

1. Defining Frequency | 频率的定义

Frequency f is the number of complete oscillations, rotations or wave cycles that occur in one second. The SI unit is the hertz (Hz), where 1 Hz is exactly one cycle per second.

频率 f 是每秒发生的完整振动、旋转或波动循环的次数。其 SI 单位是赫兹 (Hz)，1 Hz 恰好等于每秒一个周期。

If an object completes N cycles in time t, the average frequency is f = N / t. For steady periodic motion, this gives a single constant value.

如果一个物体在时间 t 内完成 N 个周期，其平均频率为 f = N / t。对于稳定的周期性运动，这给出一个恒定值。

f = 1 / T

Here T is the period, which is the time for one complete cycle. This equation is the starting point for nearly all frequency calculations in CIE A-Level Physics.

这里 T 是周期，即完成一个完整循环所需的时间。这个方程是 CIE A-Level 物理中几乎所有频率计算的起点。

2. Period and Frequency | 周期与频率

The period T is the time taken for one complete cycle. It is measured in seconds. Period and frequency are inverse quantities: a large frequency means a small period, and vice versa.

周期 T 是完成一个完整循环所需的时间，单位为秒。周期和频率互为倒数：频率越大，周期越小，反之亦然。

T = 1 / f

A pendulum with T = 2.0 s has f = 0.50 Hz. A radio wave with f = 100 MHz has T = 1.0 × 10⁻⁸ s. Both quantities describe the same motion from different viewpoints.

周期 T = 2.0 s 的摆，频率 f = 0.50 Hz。频率 f = 100 MHz 的无线电波，周期 T = 1.0 × 10⁻⁸ s。这两个量从不同角度描述同一个运动。

Units are often the first clue in exam questions. If a value is given in hertz, it is f; if it is given in rad s⁻¹, it is ω.

单位往往是考试题中的第一线索。如果数值以赫兹给出，它是 f；如果以 rad s⁻¹ 给出，它是 ω。

3. Angular Frequency | 角频率

Angular frequency ω is the rate at which the phase angle of a rotating or oscillating system changes. It is measured in radians per second, written rad s⁻¹.

角频率 ω 是旋转或振动系统的相位角变化的速率。它以弧度每秒为单位，写作 rad s⁻¹。

ω = Δθ / Δt

In one full cycle the phase angle changes by 2π radians. Therefore, if the period is T, the angular frequency is ω = 2π / T = 2πf.

在一个完整周期中，相位角变化 2π 弧度。因此，如果周期为 T，角频率为 ω = 2π / T = 2πf。

For uniform circular motion, Δθ/Δt is constant and is often called angular speed. The same symbol ω is used because the underlying mathematics is identical.

对于匀速圆周运动，Δθ/Δt 恒定，通常称为角速度。使用相同的符号 ω，因为背后的数学是相同的。

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