I have a question about standing waves on strings. I'll try to explain the best I can, I searched and researched the whole day yesterday but I am confused still:
- Every frequency has a single, and only one possible wavelength. This is what I come across over and over again, with no other conditions mentioned. eg. E2 is 82.407hz with a wavelength of 4.129m. The wavelength seems to be referenced as a constant, nonchanging measurement. Is this correct?
- The above is proven false with simple tuning of the guitar, where the standing wave is clearly the same length (the half-length of it from nut to bridge, from node to node) yet the frequency is changed by increasing tension. The same length of the string produces for example fundamental pitch of the note E2 and F2. Does this prove the above statement false?
- Does this mean that the wavelength of the standing wave and the wavelength of the sound that it produces can be different?
EDIT: For simplicity's sake, unless it's relevant, I am talking about the fundamental only. Also, I am assuming that the speed of sound is the same, through the air, same temperature same everything, the string are the same etc.
It is really puzzling to me how seemingly same wavelengths can create different frequency on the same guitar, with the same string. And further how a guitar with a shorter nut-to-neck distance can create the same frequency. Thanks a lot in advance for any help figuring this out.