波长和频率关系

可以使用波的许多不同特性来描述波。波长和频率是两个这样的特性。波长和频率之间的关系是，波的频率乘以它的波长得到了波的速度，我们将在下面看到。

什么是波长(wavelength)？

We have discussed what wavelength means when we were discussing the difference between Wavelength and Period. To recap; every point on a wave is oscillating. That is, every point on a wave shows some kind of regular, repetitive change in some value. For example, if you create a wave by wiggling a rope up and down, then the molecules that make up the rope are repeatedly moving up and down. If you take an electromagnetic wave, the value of electric and magnetic fields due to the wave at a point is always changing. If the wave in question is not just a short pulse, then at any given time, there can be several points on a wave that are at the same stage of oscillation. For instance, two points on the wave that reach their maximum value in oscillation simultaneously are oscillating in unison. Such points, which are always at the same stage in oscillation are said to be in phase with each other.  Wavelength is the distance between the two closest points that are in phase with each other along a wave. Thus, two adjacent peaks or two adjacent troughs on a wave are separated by a distance of one wavelength. Often, we use the Greek letter lambda ( ) to represent the wavelength of a wave:

Wavelength of a wave created by wiggling a rope up and down

请注意，我把波长称为最短距离：这仅仅是一个技术问题，因为从一个点到另一个点可以走无限多条路。波长的一些定义可能没有特别提到最短路径，但在这种情况下，定义中暗示了最短距离。

什么是频率(frequency)？

Frequency () is the number of complete oscillati*** that a wave undergoes per unit time. It is measured in units of hertz (Hz). For sound waves, the frequency is related to the pitch of the sound. The higher the frequency, the higher is the pitch. For instance, the “middle C” note is a sound wave with a frequency of 261.63 Hz. This means that to produce this note, molecules creating or tran**itting the sound wave should oscillate 261.63 times every second. The note middle D which has a higher pitch than the middle C has a frequency of 293.66 Hz. Humans can hear sounds with frequencies between about 20 – 20000 Hz. Sounds with frequencies lower than the audible range is called infrasound and the sounds with frequencies above the human hearing range are called ultrasound.

什么是波长与频率的关系(the relati***hip between wavelength and frequency)？

你可以在绳子上以更快的速度上下摆动，从而产生更高频率的波浪。当你这样做的时候，你会注意到波的波长变短了。很明显，波长和频率之间有一种关系，现在我们将试图找出这种关系到底是什么。

Period () is another quantity that we can use to characterize a wave. Period is the time taken for one complete oscillation. Since frequency measures the number of times that a wave oscillates per unit time, it follows that

由于波在一个周期内经历一次完整的振荡，波中的所有点在一个周期后返回相同的值。这是由于每个“振荡阶段”在一个周期内移动一个波长的距离，最终到达一个周期之前处于同一振荡阶段的点。换句话说，在一个周期内，一个波峰移动到它的前一个波峰在一个周期之前占据的位置，依此类推。

The speed of the wave ( ) is the distance that the wave travels per unit time. C***idering that the wave travels a distance of one wavelength during one period,

We know that  . So we can write the above equation as:

也就是说，波的速度等于它的频率乘以波长。这就是波长和频率之间的关系。

Electromagnetic waves traveling through vacuum have a speed of 3×108 m s-1. This speed is a fundamental c***tant in physics, and it is denoted by the letter . So, this equation is sometimes written as  for electromagnetic travelling through vacuum.

This equation is very useful. For example, we know that electromagnetic waves can slow down when they travel from air into glass. The frequency of the wave is determined by the original disturbance that caused the wave, so the frequency does not change when the wave goes from one medium to another. Since  , this means that in order to  maintain the same frequency while the speed is decreasing, the wavelength of the wave must be reduced as well.

The speed and wavelength of a wave changes when it travels from one medium into another.

以下视频中的动画对此进行了说明：

Image Courtesy

“Wave in a rope.” by CK-12 Foundation (File:High School Chemistry.pdf, page 178) [CC BY-SA 3.0], via Wikimedia Comm*** (Modified)