Question

Question #007d3

Answer 1

`"2.956 m"`

Explanation:

All you have to do here is to use the equation that establishes a relationship between frequency and wavelength

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

Here

• `lamda` is the wavelength of the wave
• `c` is the speed of light in a vacuum, usually given as `3 * 10^8"m s"^(-1)`

This equation shows that frequency and wavelength have an inverse relationship, i.e. when the frequency is high, the wavelength is short, and when the frequency is low, the wavelength is long.

Now, notice that the speed of light is measured in meters per second. This tells you that you need to convert the frequency of wave from megahertz to hertz, since

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

You will have

`101.5 color(red)(cancel(color(black)("MHz"))) * (10^6color(white)(.)"Hz")/(1color(red)(cancel(color(black)("MHz")))) = 1.015 * 10^8` `"Hz" = 1.015 * 10^8` `"s"^(-1)`

So, rearrange the equation to solve for `lamda`

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

Plug in your value to find

`lamda = (3 * 10^8 "m"color(red)(cancel(color(black)("s"^(-1)))))/(1.015 * 10^8color(red)(cancel(color(black)("s"^(-1))))) = color(darkgreen)(ul(color(black)("2.956 m")))`

The answer should be rounded to four sig figs, the number of sig figs you have for the frequency of the wave.

In your case, the valid option would be (a) `"2.96 m"`.