Compare 940 on the AM dial to 94 on the FM dial. Which has the longer wavelength and by what factor is it larger?
Compare 940khz and 94Mhz. What factor does the frequency vary? What factor is wavelength vary?
To compare the wavelengths of AM and FM radio frequencies, we can use the formula:
Wavelength = Speed of Light / Frequency
First, we need to convert the frequencies to their respective wavelengths.
For AM radio, the frequency is 940 on the AM dial. Generally, AM radio frequencies are measured in kilohertz (kHz), so we convert it to megahertz (MHz) by dividing by 1000:
AM frequency = 940 kHz = 0.94 MHz
For FM radio, the frequency is 94 on the FM dial. FM radio frequencies are usually measured in megahertz (MHz) directly.
FM frequency = 94 MHz
Now, we use the wavelength formula to calculate the wavelengths of each frequency.
For AM radio:
AM wavelength = Speed of Light / AM frequency
For FM radio:
FM wavelength = Speed of Light / FM frequency
The speed of light is approximately 3 x 10^8 meters per second.
Calculating the wavelengths:
AM wavelength = (3 x 10^8 m/s) / 0.94 x 10^6 Hz = 319.15 meters
FM wavelength = (3 x 10^8 m/s) / 94 x 10^6 Hz = 3.19 meters
Comparing the results, we find that the AM frequency has a longer wavelength than the FM frequency. The AM wavelength is approximately 319.15 meters, while the FM wavelength is approximately 3.19 meters.
To determine the factor by which the AM wavelength is larger, we divide the AM wavelength by the FM wavelength:
AM wavelength / FM wavelength = 319.15 meters / 3.19 meters
The factor is approximately 100 times:
319.15 meters / 3.19 meters ≈ 100
Therefore, the AM wavelength is approximately 100 times larger than the FM wavelength.