Question

compare 990 on the am dial to 92.3 on the fm. which has the longer wavelength?
the am station.
the fm station.
both stations have the same wavelength.
submit previous answers
correct
part b
by what factor is it larger?
express your answer using three significant figures.
\\( \frac { \lambda _ { a m } } { \lambda _ { f m } } = \\)

Explanation:

Step1: Recall the formula for wavelength

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

Step2: Determine the frequencies of AM and FM stations

AM frequency \(f_{AM}=990\space kHz = 990\times 10^{3}\space Hz\). FM frequency \(f_{FM}=92.3\space MHz=92.3\times 10^{6}\space Hz\).

Step3: Calculate the ratio of wavelengths

Using \(\lambda=\frac{c}{f}\), the ratio \(\frac{\lambda_{AM}}{\lambda_{FM}}=\frac{f_{FM}}{f_{AM}}\) (since \(\lambda\propto\frac{1}{f}\) when \(c\) is constant).
Substitute \(f_{AM}=990\times 10^{3}\space Hz\) and \(f_{FM}=92.3\times 10^{6}\space Hz\) into the formula:

$$ \frac{\lambda_{AM}}{\lambda_{FM}}=\frac{92.3\times 10^{6}}{990\times 10^{3}}=\frac{92300}{990}\approx93.2 $$

Answer:

\(93.2\)