Question

2. Cell phones work by receiving and emitting radiation in the range of 1.9-2.2 Giga Hertz (GHz). This is about 1.9 X 109 -2.2 X 109 Hz.
A) Based on this information, calculate the wavelength of this radiation.
B) What type of electromagnetic radiation do cell phones use?

Answer 1

A) 0.136 - 0.158 m

B) Microwaves

Explanation:

A)

For an ectromagnetic wave, there is a relationship between its frequency and its wavelength, contained in the wave equation:

$\lambda=\frac{c}{f}$

where

$\lambda$ is the wavelength of the wave

$c=3.0\cdot 10^8 m/s$  is the speed of light in a vacuum

f is the frequency of the wave

For the waves in this problem, we have:

$f_1=1.9\cdot 10^9 Hz$ is the minimum frequency

$f_2=2.2\cdot 10^9 Hz$ is the maximum frequency

Therefore, the range of corresponding wavelengths is:

$\lambda_1=\frac{3\cdot 10^8}{1.9\cdot 10^9}=0.158 m$

$\lambda_2=\frac{3\cdot 10^8}{2.2\cdot 10^9}=0.136 m$

B)

Electromagnetic waves are oscillations of the electric and the magnetic field occurring in a plane perpendicular to the direction of motion the wave.

All electromagnetic waves travel in a vacuum always at the same speed, the speed of light ($c=3.0\cdot 10^8 m/s$ ).

Electromagnetic waves are classified into 7 different types, according to their wavelength and frequency. From the longest to the shortest wavelength, we have:

Radio waves (>1 m)

Microwaves (1 mm - 1 m)

Infrared (750 nm - 1 mm)

Visible light (380 nm - 750 nm)

Ultraviolet (10 nm - 380 nm)

X-rays (0.01 nm - 10 nm)

Gamma rays (<0.01 nm)

Therefore, we see that the waves in this problem (of wavelength between 0.136 and 0.158 m) are classified as microwaves.