I am trying to learn to play the clarinet and was doing fairly well until I tried to play a tune with my granddaughters on flute and piano. My clarinet was not in tune with their instruments. I have a "Teach yourself" type of book that includes fingering. When the music indicates a "C" and I set my fingers to what the book says is a "C" it actually plays a "Bb". Why doesn't the music show a "Bb" for that fingering? Do I need to transpose all my music to enable me to play with other people on other instruments? Why did my book tell me that a certain fingering plays a "C" when it actually plays a "Bb"?
Pretty sure this is a dupe, but - the clarinet, like several other instruments, is a transposing instrument. Yours makes the sound a whole tone lower than the music says. So when you see and play a C note, a B♭ comes out. There are other clarinets, but the 'B♭' is the most common.
You'll have to either learn to play by transposing up a tone from your music, (like I did with trumpet - a similar idea), or get the piano music transposed down a tone, either physically, with a good reader - or, these days, by hitting the transpose button on the keyboard.
The reason is about professional play of similar instruments of different sizes (and therefore pitches).
Think of "C" as a finger position: you read a C, you put your fingers in that position. If you pick up a B-flat instrument or whatever, then the same finger position will play a B-flat.
It's up to the COMPOSER to figure out the right transpositions, so you don't have to transpose in your head while you're playing your part from sheet music. I mean, some pieces even have multiple instruments played by the same person!