Suppose you are standing 201 m from a radio transmitter. What is your distance from the transmitter in terms of the number of wavelengths for the following conditions?
(a) The station is broadcasting at 1150 kHz (on the AM radio band)? (1 kHz = 1 multiplied by 103 Hz.)
?? wavelengths
(b) The station is broadcasting at 98.1 MHz (on the FM radio band)? (1 MHz = 106 Hz.)
??wavelengths
c=wavelength x frequency.
3 x 10^8 = 1.150 x 10^6 Hz x wavelength.
Solve for wavelengths)in meters).
Then 200/signal wavelength = # wavelengths.
260 Hz/ms
To calculate the distance in terms of the number of wavelengths, we can use the formula:
Distance (meters) = (Speed of light)/(Frequency (Hz)).
The speed of light is approximately 3 x 10^8 m/s.
Let's calculate the distance for each condition:
(a) The station is broadcasting at 1150 kHz:
Frequency = 1150 kHz = 1150 x 10^3 Hz.
Distance = (3 x 10^8 m/s)/(1150 x 10^3 Hz).
= 260.87 meters.
So, the distance from the transmitter is approximately 260.87 meters in terms of the number of wavelengths for a frequency of 1150 kHz.
(b) The station is broadcasting at 98.1 MHz:
Frequency = 98.1 MHz = 98.1 x 10^6 Hz.
Distance = (3 x 10^8 m/s)/(98.1 x 10^6 Hz).
= 3.054 meters.
So, the distance from the transmitter is approximately 3.054 meters in terms of the number of wavelengths for a frequency of 98.1 MHz.
To find the distance in terms of the number of wavelengths, we need to use the formula:
Number of wavelengths = Distance / Wavelength
(a) Let's first find the wavelength for the frequency of 1150 kHz. We know that 1 kHz is equal to 1 * 10^3 Hz, so the frequency can be written as 1150 * 10^3 Hz.
The formula for wavelength is given by: Wavelength = Speed of light / Frequency
The speed of light is approximately 3 * 10^8 meters per second (m/s). Substituting the values into the formula, we have:
Wavelength = (3 * 10^8 m/s) / (1150 * 10^3 Hz)
Now, we can calculate the wavelength:
Wavelength = 260.87 meters
To find the distance in terms of wavelengths, we can divide the given distance of 201 meters by the wavelength:
Number of wavelengths = 201 meters / 260.87 meters
Number of wavelengths ≈ 0.77 wavelengths
Therefore, the distance from the transmitter in terms of the number of wavelengths for a station broadcasting at 1150 kHz is approximately 0.77 wavelengths.
(b) For the frequency of 98.1 MHz, we know that 1 MHz is equal to 1 * 10^6 Hz, so the frequency can be written as 98.1 * 10^6 Hz.
Using the same formula for wavelength as in part (a), we can find the wavelength:
Wavelength = (3 * 10^8 m/s) / (98.1 * 10^6 Hz)
Wavelength ≈ 3.05 meters
Now, we can calculate the number of wavelengths:
Number of wavelengths = 201 meters / 3.05 meters
Number of wavelengths ≈ 65.90 wavelengths
Therefore, the distance from the transmitter in terms of the number of wavelengths for a station broadcasting at 98.1 MHz is approximately 65.90 wavelengths.