To determine the wavelength of radio waves given a specific frequency using the inverse variation equation, we start with the formula that relates the wavelength [tex]\( x \)[/tex] and frequency [tex]\( y \)[/tex]:
[tex]\[
y = \frac{3 \times 10^8}{x}
\][/tex]
In this formula, [tex]\( y \)[/tex] is the frequency of the radio waves, and [tex]\( x \)[/tex] is their wavelength. We are given the frequency [tex]\( y \)[/tex] as:
[tex]\[
3 \times 10^9 \, \text{Hz}
\][/tex]
We need to find the corresponding wavelength [tex]\( x \)[/tex]. First, we rearrange the formula to solve for [tex]\( x \)[/tex]. This can be done by multiplying both sides by [tex]\( x \)[/tex] and then dividing by [tex]\( y \)[/tex]:
[tex]\[
y x = 3 \times 10^8
\][/tex]
[tex]\[
x = \frac{3 \times 10^8}{y}
\][/tex]
Substitute the given frequency [tex]\( y = 3 \times 10^9 \, \text{Hz} \)[/tex] into the equation:
[tex]\[
x = \frac{3 \times 10^8}{3 \times 10^9}
\][/tex]
Dividing the numbers:
[tex]\[
x = 3 \times 10^8 \div 3 \times 10^9
\][/tex]
Since [tex]\( 10^8 \)[/tex] divided by [tex]\( 10^9 \)[/tex] is [tex]\( 10^{-1} \)[/tex]:
[tex]\[
x = \frac{3}{3} \times 10^{-1} = 1 \times 10^{-1} \, \text{meters}
\][/tex]
Therefore, the wavelength [tex]\( x \)[/tex] for radio waves with a frequency of [tex]\( 3 \times 10^9 \)[/tex] Hz is:
[tex]\[
1 \times 10^{-1} \, \text{meters} \text{ or } 0.1 \, \text{meters}
\][/tex]
