We present comprehensive calculations of gravitational wave strain amplitudes for known binary pulsar systems, using data from current ground based detectors (LIGO-Virgo-KAGRA) and the upcoming space-based missions (LISA). We present detailed calculations of the characteristic gravitational wave strain values, ranging from 3.0 to 73 (times, 10^{-22}), across frequencies between 0.66 and 5.87 (times, 10^{-4}) Hz. Our post-Newtonian approximation analysis yields predicted periastron advance rates from 1.6 to 80.5 deg/yr and orbital period decay rates between −5 and −176 (upmu)s/yr for the binary pulsar population. We derive common envelope efficiency parameters ((alpha _{rm CE})) for representative progenitor scenarios within our sample, finding values between 0.63 and 1.16, with notable sensitivity to the binding energy parameter (lambda). Binary neutron star merger rates are estimated at (22.77^{+6.83}_{-6.83}) (textrm{Myr}^{-1}) for the Milky Way, corresponding to a volumetric rate of (227.71^{+68.31}_{-68.31}) (textrm{Gpc}^{-3}) (textrm{yr}^{-1}), consistent with the latest LIGO-Virgo-KAGRA observational constraints. Our results illustrate how multi-band gravitational wave observations, from LIGO/Virgo to LISA, can contribute to precise measurements of binary pulsar strain and orbital evolution histories, improving merger time predictions and constraining neutron star physics and common envelope processes.
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