Question

Calculate the wavelength of Radio 4 which broadcasts on a frequency of `"198 kHz"` ?

Answer 1

`1.51 * 10^3 \ "m"`

Explanation:

The thing to remember about wavelength and frequency is that they have an inverse relationship given by the equation

`color(blue)(ul(color(black)(lamda * nu = c))`

Here

• `lamda` is the wavelength of the wave
• `nu` is its frequency
• `c` is the speed of light, usually taken to be in a vacuum, i.e. `c = 3 * 10^8 \ "m s"^(-1)`

This basically tells you that if you multiply the wavelength and the frequency, you must always end up with the value of the speed of light,

![)

In your case, you already know the frequency of the radio waves

`"198 kHz" = 198 color(red)(cancel(color(black)("kHz"))) * (10^3 \ "Hz")/(1color(red)(cancel(color(black)("kHz")))) = 1.98 * 10^5 \ "Hz"`

As you know, you have

`"1 Hz" = "1 s"^(-1)`

which means that the frequency of the radio waves can be written as

`1.98 * 10^5 \ "Hz" = 1.98 * 10^5 \ "s"^(-1)`

Since no information was given about the value of the speed of light, you can assume that you're working with the approximation

`c = 3 * 10^8 \ "m s"^(-1)`

Rearrange the equation to solve for `lamda`

`lamda * nu = c implies lamda = c/nu`

Plug in your values to find

`lamda = (3 * 10^8 \ "m"color(red)(cancel(color(black)("s"^(-1)))))/(1.98 * 10^5 color(red)(cancel(color(black)("s"^(-1))))) = color(darkgreen)(ul(color(black)(1.51 * 10^3 \ "m")))`

The answer is rounded to three sig figs, the number of sig figs you have for the frequency of the radio waves.