Harmonics frequency question

[Ikarium]

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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?

 

[jtran7]

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