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

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,

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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.