The recommendation in the comment is a good one, Fletcher and Rossing are the definitive experts on the subject. If you are looking for a watered down text on the same topic I would recommend Physics and the Sound of Music by Rigden. I've used that and F&R to teach the course at several universities (both as a survey course and a physics major course). I think we are assuming that you want a treatment that demonstrates the use in music since you mentioned Harmony in your question.
Ridgen is non-mathematical and approaches the topic from the very bottom with little or no assumption of scientific background. I would also recommend looking at the chapters on wave mechanics and acoustics in any freshman level physics text as a reference. You'll get the basics on the physics and math in general.
The relation of harmonics to harmony theory was first investigated seriously by Herman Helmholtz and culminated in the publication of "On the Sensations of Tone" in the late 1800's. The text is available in Dover print soft cover for cheap. But that will be loaded very deep with math and physics. I think it's an interesting piece of history.