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

16.666(recurring) so 17 x

Answer 2

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

$f\alpha \frac{1}{w}$

$f = \frac{k}{w}$ , $k\neq 0$

w= 100 m and f = 3,000 kilohertz

Plug in the above values to find k

3000 = $\frac{k}{100}$

To find k, multiply both side by 100

3000(100) = k

k = 300,000

So equation becomes,

$f = \frac{300,000}{w}$

w= ? f = 500 kilohertz

500 = $\frac{300,000}{w}$

w = $\frac{300,000}{500}$

w = 600 m