波長和頻率關係

可以使用波的許多不同特性來描述波。波長和頻率是兩個這樣的特性。波長和頻率之間的關係是，波的頻率乘以它的波長得到了波的速度，我們將在下麵看到。

什麼是波長(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

請註意，我把波長稱為最短距離：這僅僅是一個技術問題，因為從一個點到另一個點可以走無限多條路。波長的一些定義可能沒有特別提到最短路徑，但在這種情況下，定義中暗示了最短距離。

什麼是頻率(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.

什麼是波長與頻率的關係(the relati***hip between wavelength and frequency)？

你可以在繩子上以更快的速度上下擺動，從而產生更高頻率的波浪。當你這樣做的時候，你會註意到波的波長變短了。很明顯，波長和頻率之間有一種關係，現在我們將試圖找出這種關係到底是什麼。

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

由於波在一個週期內經歷一次完整的振蕩，波中的所有點在一個週期後返回相同的值。這是由於每個“振蕩階段”在一個週期內移動一個波長的距離，最終到達一個週期之前處於同一振蕩階段的點。換句話說，在一個週期內，一個波峰移動到它的前一個波峰在一個週期之前佔據的位置，依此類推。

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:

也就是說，波的速度等於它的頻率乘以波長。這就是波長和頻率之間的關係。

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.

以下影片中的動畫對此進行了說明：

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)