If a chunk of matter absorbs 100 wave crests and emits 101 wave crests, then we would say that the chunk of matter created some wave crests by itself, at least one. Right?
If 100 crests go in and then 100 crests come out at slower rate, then it is possible that the waves that came out are the same as the waves that went in.
Like if we send a continuous sound wave through an air mass whose temperature is dropping, then 100 waves that went in during 1 seconds time, those same waves may come out during 2 seconds, so this changing medium halves the frequency, and doubles the duration. (And contains at least 50000 wave crests after 1000 seconds)