Why did Shmuel ask Hashem to send rain and sounds?
Rashi: Rain at this time is a sign of a curse, and Hashem is loathe to bring punishments for naught. Even so, I have the power [through my Tefilah]. I will call, and He will bring noises and rain.
Radak (16): Even though they believed in Shmuel, there were some evil people who were unsure about his words, just like they said about making Sha'ul king (10:27) 'what will this one save us?!', even though he was given via Hashem and chosen via the Urim v'Tumim or lottery. Therefore, Shmuel made a sign for them that they cannot deny.
Malbim #1: This will show that His Hashgachah clings to you. If so, you should not have chosen a king to save you via nature, since you are saved via Hashgachah. My Tefilah could have brought thunder to scare the Pelishtim, like above (7:10).
Malbim #2: Rain and sounds are good at the time of seeding, and bad in summer. Also you requested in the wrong time. If (i.e. even though) a king would be good for you after my death, and when you are under nature, it is bad for you when I am alive and Hashem protects over you.