Nostalgic
Nostalgia
This is a single kanji with an い on the end, meaning you know it's probably an adjective. What's the adjective form of nostalgia? It's nostalgic.
なつかしい
The reading is the one you learned with the kanji. Do you remember doing that? Oh man, those were the days. How 懐かしい.
懐かしい曲がスピーカーから鳴り響いていました。
A nostalgic song was echoing out of the speakers.