Gopal,

Measuring the "back-emf" is the standard method for measuring the resonant fz of a speaker. Most Test Oscillators have sufficient drive such that an additional power amp is usually not required. As few micro's cannot typically drive 2,4,and 8 Ohms, a small driver such as a LM386 or other small amp is justified.

A speaker resonant fz is not just the result of the Voice Coil resonance but also the mechanical resonance of the Spider and Cone (if you are testing "free air" resonance) and the cabinet if you are measuring the "box" load. You will have to drive the speaker to determine this.

This does not preclude Peter's technique.

Are you also going to determine the Thiele/Small characteristics?

I would suggest a "data driven" approach where you model your solution on a standard test equipment set up, observe the result and replace each function block with a micro-based solution. First build the square wave sweep generator and alternate this drive with your sine test oscillator. Observe the result. At low frequencies the "edge delay"
that results should be easily observed and detected. Now strategize your detection techique

regards,
p