  We present an analysis of NuSTAR observations of a hard intermediate state of
the transient black hole GX 339-4 taken in January 2015. As the source softened
significantly over the course of the 1.3 d-long observation we split the data
into 21 sub-sets and find that the spectrum of all of them can be well
described by a power-law continuum with an additional relativistically blurred
reflection component. The photon index increases from ~1.69 to ~1.77 over the
course of the observation. The accretion disk is truncated at around 9
gravitational radii in all spectra. We also perform timing analysis on the same
21 individual data sets, and find a strong type-C quasi-periodic oscillation
(QPO), which increase in frequency from ~0.68 to ~1.05 Hz with time. The
frequency change is well correlated with the softening of the spectrum. We
discuss possible scenarios for the production of the QPO and calculate
predicted inner radii in the relativistic precession model as well as the
global disk mode oscillations model. We find discrepancies with respect to the
observed values in both models unless we allow for a black hole mass of ~100
M_sun , which is highly unlikely. We discuss possible systematic uncertainties,
in particular with the measurement of the inner accretion disk radius in the
relativistic reflection model. We conclude that the combination of observed QPO
frequencies and inner accretion disk radii, as obtained from spectral fitting,
is difficult to reconcile with current models.
