I'm having a difficult time with the Conversion Units in my equation.
Attempting to answer this question:
My cell phone has an antenna about 10.00cm long. If this is one quarter of the wavelength of the radiation, at what frequency in Megahertz does it operate? Note that cell phones, like radio, transmit sounds via electromagnetic waves which travel at the speed of light or 3x108m/s.
I know f=v/l, but Ii am having a difficult time in getting to an answer in MegaHertz.
c = speed of light = 3.00E8 m/s
f = freq is in Hz
w = wavelength in meters.
c = fw
1/4 wavelength = 10.0 cm so 1 w = 40 cm = 0.400m
f = c/w = 3.00E8/0.4 = 7.50E8 Hz.
Now you convert to the unit you want.
7.50E8 Hz x (1 MHz/10^6 Hz) = ?
Dr Bob,
Thanks for the help with the conversion. I was missing the solution on two fronts. One was the wavelength factor and the other was the MegaHertz.
Do you know where I can find more information on "wavelength of the radiation" ? There is not a lot of specific detail in my text book.
Thanks again.
No I don't, other than the obvious of using google.com. The c = fw thing I remember from freshman physics many long years ago but I've used it thousands of times. If you know that it will take you a long way in frequency/wavelength problems.
To find the frequency in Megahertz (MHz), we can follow these steps:
1. Convert the wavelength from centimeters (cm) to meters (m).
- The wavelength is given as one-quarter of the antenna length, which is 10.00 cm.
- Convert cm to meters by dividing by 100: 10.00 cm / 100 = 0.10 m.
2. Use the formula: frequency (f) = speed of light (v) / wavelength (λ).
- The speed of light is given as 3x10^8 m/s.
- The converted wavelength is 0.10 m.
3. Substitute the values into the formula and solve for the frequency:
f = (3x10^8 m/s) / (0.10 m)
f = 3x10^8 / 0.10
f = 3x10^9 Hz (hertz)
4. Convert the frequency from hertz (Hz) to megahertz (MHz).
- To convert from Hz to MHz, divide by 10^6.
- f = 3x10^9 / 10^6 = 3000 MHz
Therefore, the cell phone operates at a frequency of 3000 MHz or 3 GHz (Gigahertz).