  In high-energy astronomical phenomena, the stochastic particle acceleration
by turbulences is one of the promising processes to generate non-thermal
particles. In this paper, we investigate the energy-diffusion efficiency of
relativistic particles in a temporally evolving wave ensemble that consists of
a single mode (Alfv\'en, fast or slow) of linear magnetohydrodynamic waves. In
addition to the gyroresonance with waves, the transit-time damping (TTD) also
contributes to the energy-diffusion for fast and slow-mode waves. While the
resonance condition with the TTD has been considered to be fulfilled by a very
small fraction of particles, our simulations show that a significant fraction
of particles are in the TTD resonance owing to the resonance broadening by the
mirror force, which non-resonantly diffuses the pitch angle of particles. When
the cutoff scale in the turbulence spectrum is smaller than the Larmor radius
of a particle, the gyroresonance is the main acceleration mechanism for all the
three wave modes. For the fast-mode, the coexistence of the gyroresonance and
TTD resonance leads to anomalous energy-diffusion. For a particle with its
Larmor radius smaller than the cutoff scale, the gyroresonance is negligible,
and the TTD becomes the dominant mechanism to diffuse its energy. The
energy-diffusion by the TTD-only resonance with fast-mode waves agrees with the
hard-sphere-like acceleration suggested in some high-energy astronomical
phenomena.
