Question

The frequency of a radio wave varies inversely with its wavelength. If a 100-meter wave has a frequency of 3,000 kilohertz, what is the wavelength of a wave that has a frequency of 500 kilohertz? Round your answer to the nearest meter.

Answer 1

Let the frequency be 'f' and wavelength be 'w'

`f\alpha (1)/(w)`

`f = (k)/(w)` ,
`k\\eq 0`

w= 100 m and f = 3,000 kilohertz

Plug in the above values to find k

3000 =
`(k)/(100)`

To find k, multiply both side by 100

3000(100) = k

k = 300,000

So equation becomes,

`f = (300,000)/(w)`

w= ? f = 500 kilohertz

500 =
`(300,000)/(w)`

w =
`(300,000)/(500)`

w = 600 m