To find the wavelength of a radio wave, you can use the relationship between the speed of the wave, its frequency, and its wavelength. The formula is given by:
\[ \text{speed} = \text{frequency} \times \text{wavelength} \]
For radio waves, the speed is typically the speed of light in a vacuum, which is approximately \( c = 3.00 \times 10^8 , \text{m/s} \).
Given the frequency \( f = 88.1 , \text{MHz} = 8.81 \times 10^7 , \text{Hz} \), we can rearrange the formula to solve for wavelength \( \lambda \):
\[ \lambda = \frac{c}{f} \]
Substituting the values:
\[ \lambda = \frac{3.00 \times 10^8 , \text{m/s}}{8.81 \times 10^7 , \text{Hz}} \]
Now, performing the calculation:
\[ \lambda \approx \frac{3.00}{8.81} \times 10^{8 - 7} \] \[ \lambda \approx 0.340 \times 10^{1} \] \[ \lambda \approx 3.40 , \text{m} \]
Thus, the wavelength of the wave used by this radio station is:
\[ \boxed{3.40 , \text{m}} \]