Why does, say, a note on a violin have a “pitch”, but the sound made when I bang a table doesn’t have a “pitch”.
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Something that has a pitch is just any sound that repeats at some frequency.
When you pluck an “A” guitar string, it vibrates 440 times per second, which creates pressure waves of air that repeat 440 times per second too. That’s its pitch.
When you bow an “A” violin string, it also vibrates 440 times per second. The type of vibration and the way the pressure waves reverberate through the instrument are really different, so the shape of the sound itself (the “timbre”) is really different, but just like the guitar string, the sound repeats itself every 1/440 of a second.
When you sing, your vocal cords are vibrating a certain number of times per second too. The shape of your mouth affects what it sounds like, but the frequency – the pitch – is just based on that fundamental vibration.
When you bang on a really solid table or clap your hands, the sound is more instantaneous – it doesn’t vibrate, so you’re just hearing the instantaneous pressure wave of air rushing away as you strike something and the air between your hand and the object moves out of the way. If there’s no periodic vibration, there’s no pitch.
When you hit an object that vibrates, though – even a little bit – it does make a pitch, but sometimes it’s too low or too high for us to perceive it that way. If you record the sound and the speed it up or slow it down, you can hear the pitch, like in this video:
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