It seems like the spectrum of the real world noise you've recorded is not the same as the spectrum of the pure noise you've added to the pure signal.
I mean if you used rand() to add white noise, why do you think a recording of a real world sound, say a recording you've made with your cell phone at a concert in the park, would have the same spectrum as rand()??? There's any number of reasons why the noise sources and spectra could be different, such as wind noise, traffic noise, crying babies, jets flying overhead, people talking, water sounds (fountains, rivers, etc.), distant trains, etc.
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