Why airlines don't allow cell phones

The Federal Aviation Administration (FAA) just announced that most electronic devices can now be used on airplanes, all the way from takeoff to landing. But you still can't make a call on your cell phone during a flight, and all devices must be set to "flight mode." Why can't you make calls on flights? To get a better understanding, let's use some trigonometry.

Airplanes communicate and navigate using a band of radio waves called the airband, which uses frequencies between 108 and 137 MHz (or megahertz). Radio waves are electromagnetic waves, or waves of light, which travel through space like the sine function. Waves with higher frequencies move up and down, or "oscillate," faster, while lower-frequency waves oscillate more slowly. Here are examples of waves that have different frequencies:

How do the frequencies of cell phones compare to those of the airband? Well, it depends on the carrier (Verizon, AT&T, etc.), but for the most part they're between 500 and 2500 MHz. So cell phones send and receive radio waves that are close to the Airband, but are slightly higher in frequency.

If you were to make a call on a plane, then the cell phone's radio waves and the airplane's radio waves would add together. The airplane's waves are probably a lot stronger than the waves coming out of your phone. So what happens if we add a very weak cell phone signal (say, at 700 MHz) to a strong airplane signal at 120 MHz?

The sum of the two waves looks pretty close to the airplane's signal. But what happens if the cell phone signal were a lot stronger?

Suddenly, the sum looks quite different from the airplane's signal, and that's what worries the FAA. While there are mathematical tools that tease apart signals with different frequencies that have been added together, pilots and officials are concerned that cell phone radio waves could still interfere with the communication and navigation of airplanes.

If cell phones instead used frequencies that were really far away from the airband, then the risk of interference would be even smaller (even if the phones emitted really strong signals). Why do you think that is?