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?(adsbygoogle = window.adsbygoogle || []).push({});

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?

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Summation of continuous band of frequencies

Loading...

Similar Threads - Summation continuous band | Date |
---|---|

A Continuous mass distribution | Jul 5, 2017 |

How to solve this partial derivative which includes a summation? | Apr 3, 2017 |

Summation Convention – Substitution Rule | Feb 16, 2016 |

Summation properties | Oct 29, 2015 |

Calculus by Spivak, Chapter 2, Problem 6, Part 3 | Jul 24, 2015 |

**Physics Forums - The Fusion of Science and Community**