  We investigate the effect of frequency on the principal eigenvalue of a
time-periodic parabolic operator with Dirichlet, Robin or Neumann boundary
conditions. The monotonicity and asymptotic behaviors of the principal
eigenvalue with respect to the frequency parameter are established. Our results
prove a conjecture raised by Hutson, Michaikow and Pol\'{a}\v{c}ik [2001 J.
Math. Biol.].
