Just got a "thought experiment" question from a colleague. The question, as phrased was: If an audio signal was composed by adding all of the frequencies in the audible range, what would it sound like? I thought it was interesting, so I attempted to solve it by integral. My calculus skills have always been suspect, however, so I would appreciate some feedback. If each component can be described as sin(f*x), where x is time and f specifies the frequency, then each moment of the resultant signal is the integral of sin(f*x) from f_low to f_high, treating x as a constant. This should simplify to F(x) = cos(f_low*x)/x - cos(f_high*x)/x which describes the entire signal. Anything wrong with that?