Question

Question #12271

Answer 1

The wavelength for that particular FM frequency is `"2.891 m"`.

Every time you have to calculate frequency when given wavelength, or, such as in this case, wavelength given frequency, you must remember one equation

`c = lamda * nu`, where

`c` - the speed of light - exactly `"299,792,458 m/s"`;
`lamda` - wavelength;
`nu` - frequency;

This equation describes the inverse relationship frequency and wavelength have.

In this case, frequency is given to you in MHz. Before going to the equation, remember to convert this value into Hz, or better yet into `"s"^(-1)`

`"103.7 MHz" * (10^(6)"Hz")/("1 MHz") * (1 s^(-1))/("1 Hz") = "103,700,000 s"^(-1)`

Now just plug this into the equation

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

`lamda = ("299,792,458 m/s")/("103,700,000 s"^(-1)) = "2.891 m"`

Don't worry about the speed of light, its exact value will be given to you. However, it would be an advantage to know that the speed of light is usually used as `3 * 10^(6)"m/s"`.