Resonance

共振

In sound applications, a resonant frequency is a natural frequency of vibration determined by the physical parameters of the vibrating object. This same basic idea of physically determined natural frequencies applies throughout physics in mechanics, electricity and magnetism, and even throughout the realm of modern physics. Some of the implications of resonant frequencies are:

在声学应用中，共振频率是由振动物体的物理参数决定的自然振动频率。这一基本概念——由物理因素决定的自然频率——也适用于物理学中的力学、电磁学，甚至现代物理的整个领域。共振频率的一些影响包括：

1. It is easy to get an object to vibrate at its resonant frequencies, hard to get it to vibrate at other frequencies.

使物体在共振频率上振动很容易，但在其他频率上振动则困难。

Example

示例

2. A vibrating object will pick out its resonant frequencies from a complex excitation and vibrate at those frequencies, essentially "filtering out" other frequencies present in the excitation.

振动物体从复杂的激励中选择其共振频率并在此频率上振动，基本上‘滤除’了激励中其他频率。

Example

示例

3. Most vibrating objects have multiple resonant frequencies.

大多数振动物体都有多个共振频率。

Example

示例

Ease of Excitation at Resonance

共振时的激发容易程度

It is easy to get an object to vibrate at its resonant frequencies, hard at other frequencies. A child's playground swing is an example of a pendulum, a resonant system with only one resonant frequency. With a tiny push on the swing each time it comes back to you, you can continue to build up the amplitude of swing. If you try to force it to swing at twice that frequency, you will find it very difficult, and might even lose teeth in the process!

使物体在它的共振频率上振动很容易，而在其他频率上则很难。儿童游乐场的秋千是一个 pendulum 的例子，这是一个只有单一共振频率的共振系统。每次秋千返回时给予它一个轻微的推力，你可以持续增加秋千的振幅。如果你尝试以两倍于该频率来强迫它振动，你会发现非常困难，甚至可能在过程中失去牙齿！

Swinging a child in a playground swing is an easy job because you are helped by its natural frequency.

在游乐场荡秋千是一件容易的事，因为你会借助其自然频率。

But can you swing it at some other frequency?

但你能以其他频率摆动它吗？

Picking out resonant frequencies

挑选共振频率

A vibrating object will pick out its resonant frequencies from a complex excitation and vibrate at those frequencies, essentially "filtering out" other frequencies present in the excitation.

If you just whack a mass on a spring with a stick, the initial motion may be complex, but the main response will be to bob up and down at its natural frequency. The blow with the stick is a complex excitation with many frequency components (as could be shown by Fourier analysis), but the spring picks out its natural frequency and responds to that.

如果你只是用棍子敲击弹簧上的一个质量，初始运动可能很复杂，但主要响应将是以它的自然频率上下振动。用棍子敲击是一个包含许多频率成分的复杂激励（如傅里叶分析所示），但弹簧会选出它的自然频率并对此作出响应。

振动物体从复杂的激励中选择其共振频率并在此频率上振动，基本上‘滤除’了激励中其他频率。