Question

a vhf television station assigned to channel 18 transmits its signal using radio waves with a frequency of 494 mhz. calculate the wavelength of the radio waves. be sure your answer has the correct number of significant digits.

Explanation:

Step1: Recall the wave - speed formula

The formula that relates the speed of a wave (\(c\)), its frequency (\(f\)) and its wavelength (\(\lambda\)) is \(c = \lambda f\), where the speed of light (for electromagnetic waves like radio waves) \(c=3.00\times 10^{8}\space m/s\). We need to solve for \(\lambda\), so we can re - arrange the formula to \(\lambda=\frac{c}{f}\).

Step2: Convert the frequency to SI units

The frequency \(f = 494\space MHz\). Since \(1\space MHz=10^{6}\space Hz\), then \(f = 494\times 10^{6}\space Hz=4.94\times 10^{8}\space Hz\) (or \(s^{- 1}\)).

Step3: Calculate the wavelength in meters

Substitute \(c = 3.00\times 10^{8}\space m/s\) and \(f = 4.94\times 10^{8}\space s^{-1}\) into the formula \(\lambda=\frac{c}{f}\).
\(\lambda=\frac{3.00\times 10^{8}\space m/s}{4.94\times 10^{8}\space s^{-1}}\)
\(\lambda=\frac{3.00}{4.94}\space m\approx0.607\space m\)

Step4: Convert the wavelength from meters to millimeters

We know that \(1\space m = 1000\space mm\). So to convert meters to millimeters, we multiply by \(1000\).
\(\lambda=0.607\space m\times1000\space mm/m = 607\space mm\)

Answer:

\(607\)