The behavior of the low-frequency electromagnon in multiferroic DyMnO3 has been investigated in external magnetic fields and in a magnetically ordered state. Significant softening of the electromagnon frequency is observed for external magnetic fields parallel to the a-axis (BIIa), revealing a number of similarities to a classical soft mode behavior known for ferroelectric phase transitions. The softening of the electromagnon yields an increase of the static dielectric permittivity which follows a similar dependence as predicted by the Lyddane-Sachs-Teller relation. Within the geometry BIIb the increase of the electromagnon intensity does not correspond to the softening of the eigenfrequency. In this case the increase of the static dielectric permittivity seem to be governed by the motion of the domain walls. ; Comment: 5 pages, 4 figures