Question

Question #1f525

Answer 1

`"250 m"`

Explanation:

This is a fairly straightforward frequency and wavelength problem, but you have to make sure that you keep track of the units given to you.

As you know, frequency and wavelength have an inverse relationship described by the equation

`color(blue)( lamda * nu = c)" "`, where

`lamda` - the frequency of the wave
`nu` - its frequency
`c` - the speed of light in vacuum, usually given as `3 * 10^8"ms"^(-1)`

Basically, an inverse relationship means that longer wavelengths will correspond to lower frequencies, and shorter wavelengths to higher frequencies.

Now look at the units given to you for the frequency of the wave. As you know

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

Notice, however, that you have kilohertz, which means that you will have to use the conversion factor

`"1 kHz" = 10^3"Hz"`

when you plug your value into the above equation. So, rearrange to solve for `lamda`

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

`lamda = (3 * 10^8"m" color(red)(cancel(color(black)("s"^(-1)))))/(1200 * 10^3color(red)(cancel(color(black)("s"^(-1))))) = color(green)("250 m")`

This wavelength and its corresponding frequency are located in the radio waves region of the electromagnetic spectrum.

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