If the first harmonic has a frequency of 1 does that mean the fourth harmonic would have a frequency of 4 and a wavelength of 1/4 the first harmonic?
I'm trying to come up with an answer by putting variables into the L = (n x wavelength)/2 which is the equation of harmonics in a open end air column. (You just have to identify which scenario it is first, is it an open end air column or closed end air column?).
lets say
L the length of the column or string = 2m
V = 8m/s
n = 1
open end air column
in this situation you get...
2 = 1 x wavelength /2
so the wavelength is 4m therefore the frequency is 2 and velocity is 8m/s
now by changing it to the 4th harmonics we get...
2 = 4 x wavelength /2
so the wavelength is now 1 which is 1/4 of the wavelength of the 1st harmonic
as for the frequency by rearranging the equation L = (n x wavelength)/2 we can get...
f = nv/2L
plugging numbers in we get ...
f = 4 x 8 / 2 x 2
and so we find that the frequency of the 4th harmonic to be 8, which is 4 times the first harmonic frequency
hope this helps
