  The detection of gravitational waves from the merger of binary black holes by
the LIGO Collaboration has opened a new window to astrophysics. With the
sensitivities of ground based detectors in the coming years we can only detect
the local black hole binary mergers. The integrated merger rate can instead be
probed by the gravitational-wave background, the incoherent superposition of
the released energy in gravitational waves during binary-black-hole
coalescence. Through that, the properties of the binary black holes can be
studied. In this work we show that by measuring the energy density
$\Omega_{GW}$ (in units of the cosmic critical density) of the
gravitational-wave background, we can search for the rare $\sim 100 M_{\odot}$
massive black holes formed in the Universe. In addition, we can answer how
often the least massive BHs of mass $> 3 M_{\odot}$ form. Finally, if there are
multiple channels for the formation of binary black holes and if any of them
predicts a narrow mass range for the black holes, then the
gravitational-wave-background spectrum may have features that with the future
Einstein Telescope can be detected.
