I have a question that gives me velocity (v), tension (T), density of a metal st

Question

I have a question that gives me velocity (v), tension (T), density of a metal string (u), and the length of the string (l). It then asks me three questions: a) what is the fundamental frequency (please give equation so I can plug numbers in) b) what is the frequency of the first harmonic (also please give the equation) c) explain how frequencies and harmonics relate using fractions and showing the difference in the set up of each equation. I have a question that gives me velocity (v), tension (T), density of a metal string (u), and the length of the string (l). It then asks me three questions: a) what is the fundamental frequency (please give equation so I can plug numbers in) b) what is the frequency of the first harmonic (also please give the equation) c) explain how frequencies and harmonics relate using fractions and showing the difference in the set up of each equation.

Explanation / Answer

a) fundemental frequency, f = v/lamda

= sqrt(T/mue)/(2*L)

v --> wave speed
lamda --> wavelength
T --> Tension in the string
mue --> linear mass density of the string.
L --> length of te string.

b) First harmonic frequency = fundamental frequency

= sqrt(T/mue)/(2*L)

c)

nth harmonic frequency, f_n = n*sqrt(T/mue)/(2*L)

here n --> no of loops with whihc the string is vibrating.

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