A radio station's channel, such as 100.7 FM or 92.3 FM, is actually its frequency in megahertz (MHz), where 1 MHz =10^6 Hz}. Calculate the broadcast wavelength of the radio station 98.70 FM.
can someone please explain this question for me, i tried several times and all 3 of my answers were wrong, i don't understand how to approach this problem.
my answers i got were 30, 300 and 3*10^-7 which were all wrong.
i understand you have to use the c=f*wavelength formula though
ok.
c = f*w
3.00 x 10^8m/x = 98.70 x 10^6 Hz x w
w = 3E8/98.70E6 = 3.04 meters. That's about right because I know 144-148 MHz is in the 2 meter radio band.
To calculate the broadcast wavelength of a radio station, you can use the formula: wavelength = speed of light / frequency.
The speed of light is a constant value, which is approximately 3 x 10^8 meters per second (m/s). The frequency of the radio station is given in megahertz (MHz), but we need to convert it to hertz (Hz).
To convert megahertz to hertz, we use the conversion factor that 1 MHz = 10^6 Hz. So, for example, 100.7 MHz would be equal to 100.7 x 10^6 Hz.
Now, let's solve the problem step by step:
1. Convert the frequency to hertz:
Since the given frequency is 98.70 MHz, we can convert it to Hz by multiplying it by the conversion factor.
Frequency = 98.70 MHz x 10^6 Hz/MHz = 98.70 x 10^6 Hz.
2. Plug the values into the formula and calculate the wavelength:
Wavelength = speed of light / frequency.
Wavelength = (3 x 10^8 m/s) / (98.70 x 10^6 Hz).
Now, you can perform the calculation to find the wavelength.
Wavelength = (3 x 10^8) / (98.70 x 10^6) = 3.0375 meters (approximately).
Therefore, the broadcast wavelength of the radio station 98.70 FM is approximately 3.0375 meters.