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Why is the range of an FM signal shorter than AM signal? I thought it was due to the high frequency of FM signal getting absorbed by physical barriers. Is it so? Does power of a signal has any role to do with range?

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    \$\begingroup\$ FM and AM are just modulation techniques and have nothing to do with frequency. Please be more specific. \$\endgroup\$ – Majenko Dec 21 '14 at 10:15
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If you are comparing AM and FM standard broadcast bands then there are a couple of reasons. AM broadcast is typically about 1MHz and FM about 100MHz and this makes a big difference.

In free space (no obstacles like the earth), the power loss from a transmiting antenna to a receiving antenna (assuming perfect isotropic antennas) is: -

Loss (dB) = 32.45 + 20\$log_{10}\$(f) + 20\$log_{10}\$(d)

Where f is in MHz and d is in kilometres. This equation tells you how many dB of power loss you can expect at a given distance with a given carrier frequency.

If f = 1MHz the 1st term becomes 0dB. However, if f = 100MHz then the 1st term becomes 40dB i.e. 100MHz transmissions incur 40dB more loss at the receive antenna compared to 1MHz transmissions.

It's not that less power is transmitted but that the receiving antenna has a smaller aperture to capture power heading its way. The aperture is a measure of surface area i.e. an antenna operating at lower frequencies has a bigger effective surface area in which to capture power and convert to an electrical signal.

The 2nd reason is due to the ionosphere - signals at or about 1MHz can readily bounce off the ionosphere back to earth whereas at 100MHz, there is very little signal reflection back to earth.

See also this answer and this answer for further info.

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