If your home is at the behind the radio station at the foot of a mountain , you can receive AM but not FM. Your need to know the relative wavelength of AM and FM , so pick a familiar FM station like 98.7MHz. Calculate the wavelength ,knowing speed of electromagnetic wave as 3x power 8 meter per s, is 3m . This wavelength is small in comparison to the size of the mountain and therefore FM is not diffraction to a large extent . Your house will not be able to receive the signal , as the wave do not bend inwards after passing the mountain. On the other hand AM trasmits radio waves of longer wavelength which are of the magnitude comparable to the size of the mountain and is diffracted as it pass the mountain . You would be able to receive the AM radio transmissions. Mobile transmissions signals are of very short wavelength and therefore do not expect diffraction through very large objects like builidings and hills . To solve this problem there are lots of transmitters to provide coverage fo a particular area.
