We continue our study of waves and oscillations observed in sunspots using
an improved method for enhancing the waves, giving the opportunity to ident
ify them and determine their properties in far H alpha wings. We found that
the running penumbral waves are observable at least up to the formation he
ight of the H alpha +/- 0.5 Angstrom line, but not in the H alpha +/- 0.75
Angstrom or the Fe I +/- 0.12 Angstrom. We found a time lag between the wav
es in the blue and the red wing of the H alpha line corresponding to a phas
e shift of 180 degrees, that indicates a pure Doppler shift of the line. Th
ere is a lag in the propagation of the waves seen at H alpha center and at
H alpha wings. Also there is a lag in the variation of the umbral oscillati
ons as they are observed from lower to higher atmospheric layers. The corre
lation between umbral oscillations at various atmospheric heights and runni
ng penumbral waves strongly indicates that the latter are excited by photos
pheric umbral oscillations and not the chromospheric ones. We found a new c
ategory of photospheric waves that originate at approximately 0.7 of the di
stance between the umbra and the penumbra boundary and propagate beyond the
outer penumbra boundary with a velocity of the order of 3-4 km s(-1). Furt
her, we found 3 min penumbral oscillations apparent in the inner penumbra a
t lower chromospheric layers (far H alpha wings).