  Stars that are both pulsating and eclipsing offer an important opportunity to
better understand many of the physical phenomena that occur in stars, because
it is possible to measure the pulsation frequencies of stars for which the
masses and radii are known precisely and accurately. KIC 9851944 is a
double-lined detached eclipsing binary containing two F-stars which show both
pressure and gravity mode pulsations. We present an analysis of new
high-resolution spectroscopy of the system and high quality light curves from
the Kepler and TESS space missions. We determine the masses and effective
temperatures of the stars to 0.6% precision, and their radii to 1.0% and 1.5%
precision. The secondary component is cooler, but larger and more massive than
the primary so is more evolved; both lie inside the {\delta} Scuti and {\gamma}
Doradus instability strips. We measure a total of 133 significant pulsation
frequencies in the light curve, including 14 multiplets that each contain
between 3 and 19 frequencies. We find evidence for tidal perturbations to some
of the p- and g-modes, attribute a subset of the frequencies to either the
primary or secondary star, and measure a buoyancy radius and near-core
rotational frequency for the primary component. KIC 9851944 is mildly
metal-rich and MIST isochrones from the MESA evolutionary code agree well with
the observed properties of the system for an age of 1.25 Gyr.
