Question

compare 930 on the am dial to 92.9 on the fm. which has the longer wavelength?
the fm station.
the am station.
both stations have the same wavelength.

Explanation:

Step1: Recall the relationship between frequency and wavelength

The speed of light \(c = \lambda f\), where \(c\) is the speed of light (\(c = 3\times10^{8}\space m/s\)), \(\lambda\) is the wavelength and \(f\) is the frequency. So, \(\lambda=\frac{c}{f}\).

Step2: Determine the frequencies of AM and FM stations

AM frequencies are in the range \(535 - 1700\space kHz\). So, for the AM station with \(f_{AM}=930\space kHz = 930\times 10^{3}\space Hz\).
FM frequencies are in the range \(88 - 108\space MHz\). So, for the FM station with \(f_{FM}=92.9\space MHz=92.9\times 10^{6}\space Hz\)

Step3: Compare the wavelengths using the formula \(\lambda=\frac{c}{f}\)

Since \(c\) is constant, \(\lambda\propto\frac{1}{f}\).
Because \(f_{AM}\lambda_{FM}\) (using \(\lambda=\frac{c}{f}\))

Answer:

The AM station.