We describe the operation of a laser cooled Rb-87 frequency standard and pr
esent a new measurement of the Rb-87 ground state hyperfine frequency with
a relative accuracy of 2.4 X 10(-15), by comparison with a Cs fountain prim
ary standard. The measured frequency is 6 854 682 610,904 333(17) Hz;, An e
valuation of the frequency shift induced by cold collisions gives Delta nu/
nu(Rb) (-7.2 +/- 20) X 10(-24)(n) over bar, where (n) over bar is the avera
ge atomic density in cm(-3). With our present la uncertainty of 10(-15) thi
s measurement is still compatible with 0 and about 300 times smaller than f
or Cs-133. We also report a test of a possible variation of the fine struct
ure constant at the level of 2.7 X 10(-14)yr(-1), comparing Rb and Ca cold
atom fountains.