The length is based on the wavelength of the signal. One may
easily make a dipole custom-tuned for a given station.
Here's the basics:
http://www.electronics-radio.com/articles/radio/antennas/dipole/fm-dipole-antenna.php
... and a calculator
http://www.sengpielaudio.com/calculator-radiofrequency.htm
Each leg of the dipole should be 1/4 wavelength. A generic, store-bought FM dipole is (probably!) tuned for FM mid-band. If you are only interested to 91.7 MHz, all you need to do is calculate the wavelength of 9.17 x 10^7 cycles per second and divide by 4!
91.7 MHz = 9.17 x 10^7 cycles/sec
(2.998 x 10^8 meters/sec) / (9.17 x 10^7 cycles/sec) = 3.27 meters
3.27 meters/4 = 0.8175 meters => 32.18 inches per leg of the dipole
Here's another calculator (geared more for hams than for FM listening,but the calculator's still applicable):
http://www.radiobrandy.com/dipole1.html
EDIT: Per the previous post -- the problem with amplifiers is that by definition they amplify both the signal
and the noise; they do not improve the signal to noise ratio; it will take an antenna with more gain (and/or improved directionality) to improve the signal to noise ratio.
... and, yes, the "reception pattern" of a T-shaped dipole is a figure 8; the maximum sensitivity will be on either side of the stretched-out dipole; there'll be essentially no reception from the "ends" of the dipole.
PS The good old-fashioned TV "rabbit ear" antenna was a tuneable dipole and will work fine, too!
EDIT^2: that second on-line calculator returns a smaller value for the length (0.78 meters per leg); not sure why
