  We compute the stochastic gravitational wave (GW) background generated by
black hole-black hole (BH-BH) hyperbolic encounters with eccentricities close
to one and compare them with the respective sensitivity curves of planned GW
detectors. We use the Keplerian potential to model the orbits of the encounters
and the quadrupole formula to compute the emitted GWs. We take into account
hyperbolic encounters that take place in clusters up to redshift $5$ and with
BH masses spanning from $5 M_{\odot}$ to $55 M_{\odot}$. We assume the clusters
to be virialized and study several cluster models with different mass and
virial velocity, and finally obtain an accumulative result, displaying the
background as an average. Using the maxima and minima of our accumulative
result for each frequency, we provide analytical expressions for both
optimistic and pessimistic scenarios. Our results suggest that the background
from these encounters is likely to be detected by the third-generation
detectors Cosmic explorer and Einstein telescope, while the tail section at
lower frequencies intersects with DECIGO, making it a potential target source
for both ground- and space-based future GW detectors.
