Generally, you write your own program notes for that kind of thing. I would suggest it because you will learn more about the music you are playing.
You will need to mention:
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who wrote the piece: Paul Hindemith, a German.
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when they lived: 20th century, and when they wrote the piece: 1949
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where they wrote it: he was in America at this stage of his life
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what distinguishes the piece or the composer: Hindemith wrote in a unique style which retained tonality but was non-diatonic; instead of all 12-tones having equal importance as in serialist music of Schoenburg and other early 20th century composers, Hindemith arranged the 12 tones in order from most consonant to most dissonant; Hindemith also had an interesting relationship to the Nazi regime before he moved to America; the double bass sonata is an example of his tendency to compose for unusual or uncommon ensembles.
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why you are playing it: you're teacher probably chose it for you so you don't really know why, but make something up so the audience or the examiner thinks you're making a informed decision. Example: say you chose this piece because it represents a musical reaction to the Jewish holocaust of WWII, and that Hindemith's not-quite-atonal-but-not-quite-tonal compositional technique symbolizes the way in which the Nazi government systematized chaos in its concentration camps.
Look at the Wikipedia article on Paul Hindemith
here.
Like I said, you will have to put together your own program notes for the recital. There is no way around it; you will just have to learn a bit about Hindemith and his music. There isn't much on the bass sonata itself, but there is much on Hindemith and his music in general, so you should focus on him rather than just the sonata.
I hope this helps you!!