I am studying the physics related to playing guitar. I need to understand the relationship between the fundamental frequency of a guitar string and its harmonics.
For e.g., the top string has the fundamental frequency (E2~82.4hz). When one plucks the top string the output is a mix of the fundamental frequency and its harmonics. I need to understand the relationship between the amplitude of the fundamental frequency (82.4 Hz in this case) and the amplitude of harmonics (164.8 Hz, 247.2 Hz, 329.6 Hz and so on..)
I have been reading a lot on the internet (including this forum) and most people suggest that fundamental frequency should have the highest amplitude and the amplitude should keep decreasing with increasing harmonics.
However, my experiments suggest that this might not be true. For e.g., when I play the bottom string (E2 ~ 82.4 Hz), the largest amplitude in my output (through audacity) is around 247.2 Hz (third harmonic!). Is this possible or there is some problem with my guitar instrument?
EDIT4: Thanks for the responses. I understand that some issues could be around the guitar, recording instrument, and even the recording room. However, the important question is - In case of a guitar, what is a realistic (or most probable) relationship between a fundamental and its harmonics? (assuming a normal scenario, similar to when we hear someone play). I need to come up with the most probable mathematical relationship.
The output frequency distribution for plucking E2 string is:
EDIT: Another sample for E2 string pluck (after properly checking the tuning and ensuring no other string vibrates):
EDIT2: Sample for E2 when the string is plucked close to the center instead of near the bridge:
EDIT3: Sample for E4 (330 Hz - top most string) has highs at second and third harmonic. Sample for B open string (250 Hz):