2 vibrating strings and harmonics questions

AI Thread Summary
Two ukulele strings of equal length and mass are tuned such that the first string vibrates at twice its fundamental frequency, matching the frequency of the second string vibrating at three times its fundamental frequency. The tension of the first string is given as 60 N. To find the tension of the second string, the relationship 2f1 = 3f2 is established, where f1 and f2 are the fundamental frequencies of the first and second strings, respectively. The formula f = (1/2L)√(T/m/L) is used to relate frequency, tension, and mass per unit length. The discussion concludes with a successful adjustment for harmonics to solve for the tension F2 of the second string.
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Homework Statement


Two ukulele strings, of equal length and mass are tuned so that the first string, when it vibrates at twice its fundamental frequency, has the same frequency as the second string when
it vibrates at three times its fundamental frequency. The tension of the first string is 60 N.
Calculate the tension F2 of the second string.
Answer in units of N.


Homework Equations


f=(1/2L)Sqrt(T/m/L)


The Attempt at a Solution


so here i am stuck as i tried to set 2f1=3f2
how do i adjust for the harmonics?
 
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You can use the formula

f = \frac{p}{2L}\sqrt{\frac{T}{m/L}} where p is the number of harmonics.
 
thanks yeah i got it
 

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