Question

What is the frequency of radiation with a wavelength of `19.5` `cm`?

Answer 1

For electromagnetic radiation `c=flambda`

Rearranging, `f=c/lambda=(3xx10^8)/0.195=1.54xx10^9` `Hz`

Explanation:

First convert the wavelength to the SI unit: `lambda=0.195` `m`

Now use `v=flambda`, but remember that for electromagnetic radiation `v=c=3.0xx10^8` `ms^-1`.

Answer 2

`f = 1.53xx10^9"Hz"`

Explanation:

Assuming that the radiation is electromagnetic, we represent its speed with the letter, `C`, and use the following value:

`C = 3.0xx10^8"m/s"`

Wavelength is represented using the Greek letter lambda, `lambda`, and it is always in units of distance. To be consistent with the units of our speed number, we should convert centimeters to meters:

`lambda = 19.5"cm" to 1.95xx10^-1"m"`

Frequency is represented by many letters; the one that I prefer is `f` it is in the units of Hertz, `"Hz"` the SI equivalent of `"Hz"` is `"s"^-1`, therefore, we can remember that frequency fits into the equation because distance multiplied by seconds`"^(-1)` gives units that are consistent with speed.

Here is an equation that shows this relationship:

`C = lambdaf`

Solve for `f`:

`f = C/lambda`

Substitute in our known values:

`f = (3.0xx10^8"m/s")/(1.95xx10^-1"m")`

`f = 1.53xx10^9"Hz"`