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"This is my composition." lolz...

Any brass instrument would make you easily familiar with that interval, but to a lesser degree, most instruments offer rather natural access to it (such as strings by use of natural harmonics). It appears already rather low in the harmonic series, so it's not usually too difficult to get. It is merely dependent on harmonical/melodical context. There's no single, clearly-defined frequency ratio for either interval that would distinguish them fundamentally. The exact "size" of an augmented 2nd or a minor 3rd would depend entirely on the music it is used in and on performative practice. So when people say they "like the sound of an augmented 2nd", they aren't truly speaking of -sound- that is distinct from a minor third, but of a certain implied context (particularly, the aug 2nd implies an interval that tends towards an outward resolution rather than being a consonance).