# Period for electromagnetic waves

1. May 10, 2005

### convict11

Hi, I have a couple of questions here I am having a little bit of difficulty with.

1) What is the wavelength of an X-ray that has a period of 1.30x10e-10s?

2) A certian EMR has a wavelength of 2.14x10e-5m in air. What is the wavelength is water(n = 1.33)?

I am not looking for the answers as I prefer to be able to understand the questions and how the answers are correct but I have searched the the textbook on this unit about magnetic fields and electric fields but can not find anything of wavelengths and periods. If anyone could tell me the equation to use or anything it would be great

All I know is that Speed of wave = Frequency * Wavelength

Is the period the frequency? and the speed of wave would be the speed of light?

2. May 10, 2005

### quasar987

Almost. The frequency is how many oscillations the wave goes through in a second. The period is the time it takes the wave to complete one oscillation. A little proportionality relation shows that

$$\frac{f}{1s}=\frac{1}{T}$$

where T is the period, and f the frequency.

Yes, but the speed of light varies depending on the medium it travels in. You ought be have a formula relating speed of light of wavelenght as a function of the refractive index n somewhere in your notes or book.

3. May 11, 2005

### scholzie

In order to understand some of the methods of solving the questions you asked, it is often very helpful to do a unit analysis on a piece of paper. If you know the units of certain variables (e.g. frequency, period, etc) it is often very simple to see the relationship. For instance, if you know the frequency is in the units [1/s] and that period is in the units , it's easy to see that there's an inverse relationship.

You noted that $v=f\lambda$. If you do a unit analysis on that, you see that you will get $[m/s]=[1/s][m]$, an the units work out to equal eachother. If you're ever stumped as to how an equaton should look, or which variables you might need to use, or you have a question along the lines of "is the period the frequency," a unit analysis can often provide a quick and easy answer.

In response to your second problem, you have an index of refraction n. n is defined as the ratio of the speed of light in vacuum to the speed of light in the medium in question. In this case, the speed of light in vacuum is 1.33 times faster than the speed of light in the medium. This essentially means that all of the waves will propogate at c/1.33 through the medium, and therefore the wavelengths will also be that much smaller. It's a simple multiplication/division factor on $\lambda$

4. May 11, 2005

Thanks a lot