Want to measure frequency response of speaker

The main concern I have is that your speaker is producing Audio waves, while your inductor would be picking up changes in magnetic field going through it. So I don't think it's the best setup for measuring the speaker (audio) response. On the other hand, a microphone picks up sound so is better suited for this task. Yes, the microphone will add it's own response to the output you get, but that's going to be an issue with any transducer that is not characterized and calibrated over the frequency range you're expecting.

The best way to measure the frequency response of a loudspeaker is with a small (12mm diameter or less) high quality capacitor microphone.

This directly measures the sound produced by the speaker.

Measuring speakers is difficult because the sound level varies spatially and is affected by the environment. You can make measurements in an anechoic chamber but this will not give the same results as a user of the speaker will experience.

There are many books on this subject.

MK

Catwell  Check out this mic idea.....

https://www.youtube.com/watch?v=Ptbd3RWkwkg

Please explain your concept how an aircore inductor detects sound wave frequency ? 

Over here I am not detecting sound wave, All I am trying to do is measure alternating magnetic field of the speaker transducer coil. Since the speaker is a mechanical device. I expect the movement of speaker di-frame to be picked up as increased intensity in magnetic field by the pickup coil placed near to it at all the frequency of sound spectrum.

My suspicion is that this inductor coil is going to create mutual inductances apart from other effects that are going to distort the speaker output.

You can also take a look at app notes measuring TS speaker parameters for inspiration 

sbacoustics.com/.../Measuring-Thiele-Small-parameters.pdf

 manojroy123  You are on the right track, but with the wrong tools. Back in the day, I worked for a little company called Hughes Aircraft, I used to deal with test equipment that they used to test communications satellites. The nice thing is they had an unused Anaholic Chamber or a chamber without echoes. I had a few speakers to test which sounded better in an enclosure. that I had picked up. First, your inductor measures magnetism, not sound pressure as in sound. Second I used a "calibrated" microphone.  This is now found on some high-end stereo gear involved in balancing your Dolby system with "Pink Noise". My Yamaha DSR-100 Pro is old school It me a week-end to decide to buy it.  For the folks to have to know it was Sound Trek in Metairie, LA. 

So you have your microphone and your speaker. (the book with the microphone tells you how far to place it.) The microphone was connected to an HP 141 Spectrum Analyzer 20hz -300kHz, and a distortion analyzer as well. The best microphone would be the Directional Condenser Microphone. Anyway good luck, this is best I got ~~ Cris H. 

 javagoza I don't know about that I really depends on the distance between the two objects. also, I might agree if the coils were not parallel ie one is || this, and the other is = Sorry for the pictures but its the best I got. ~~ Cris H

 manojroy123 my thought is that you are falling down a rabbit hole. No what you need to measure is sound pressure and that Is done with a microphone. ~~Cris. H. .