Two radio waves are used in the operation of a cellular telephone. To receive a

Question

Two radio waves are used in the operation of a cellular telephone. To receive a call, the phone detects the wave emitted at one frequency by the transmitter station or base unit. To send your message to the base unit, your phone emits its own wave at a different frequency. The difference between these two frequencies is fixed for all channels of cell phone operation. Suppose the wavelength of the wave emitted by the base unit is 0.34442 m and the wavelength of the wave emitted by the phone is 0.36032 m. Using a value of 2.9979 x 108 m/s for the speed of light, determine the difference between the two frequencies used in the operation of a cell phone. Give your answer to four significant figures. Number Units the tolerance is +/-6%

Explanation / Answer

Speed of light, c = 2.9979 x 10^8 m/s

lemda1 = 0.34442 m

lemda2 = 0.36032 m

Now, use the expression -

c = f * lemda

so for the first frequency -

f1 = c / lemda1 = (2.9979 x 10^8) / 0.34442 = 8.704 x 10^8 Hz

for the second frequency -

f2 = c / lemda1 = (2.9979 x 10^8) / 0.36032 = 8.320 x 10^8 Hz

Therefore, difference in the two frequencies = f2 - f1

= 8.320 x 10^8 - 8.704 x 10^8

= 0.384 x 10^8 Hz = 38.4 x 10^6 Hz = 38.4 MHz

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