You might want to use a sinewave for your measurement as capturing AC measurements across a broad audio spectrum will require more than just a multi-meter. Many are good to about 1-KHz (1-ms) and some higher end models (that triode mentioned) are good only to about 4-KHz (250-uS).
BTW the decades old Fluke 187 & 189 were replaced years ago with with the Fluke 287 and 289 but these are in the $450 - $600 range.
The Fluke 87V is around $350 - $400.
Some lower cost models that measure True RMS AC may do what you want. In Fluke terminology look for features like Min/Max, AutoHOLD, Fast Min/Max.
