Question

a vhf television station assigned to channel 12 transmits its signal using radio waves with a frequency of 204.mhz. calculate the wavelength of the radio waves. be sure your answer has the correct number of significant digits.

Explanation:

Step1: Convert frequency unit

Convert \(204\ MHz\) to \(Hz\). Since \(1\ MHz = 10^{6}\ Hz\), then \(204\ MHz=204\times10^{6}\ Hz = 2.04\times 10^{8}\ Hz\).

Step2: Use the formula \(c = \lambda

u\)
The speed of light \(c = 3\times 10^{8}\ m/s\), and from the formula \(\lambda=\frac{c}{
u}\). Substitute \(c = 3\times 10^{8}\ m/s\) and \(
u=2.04\times 10^{8}\ Hz\) into the formula: \(\lambda=\frac{3\times 10^{8}\ m/s}{2.04\times 10^{8}\ s^{- 1}}\approx1.47\ m\).

Step3: Convert meters to centimeters

Since \(1\ m = 100\ cm\), then \(1.47\ m=1.47\times100\ cm = 147\ cm\).

Answer:

\(147\ cm\)