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Question

The A string on a string bass is tuned to vibrate at a fundamental frequency of 60.0 Hz. If the tension in the string were increased by a factor of 3, what would be the new fundamental frequency?

Answer 1

the frequency of a string is described by the equation:

f=sqrt(T/u)/(2*L)
where
T is the tension
u is the linear mass
L is the length

In the problem statement the only variable changing is the tension
so
60=K*sqrt(T)
where K is constant that absorbs all the other unknowns

when the tension is increased:
f'=K*sqrt(T*3)
or f'=K*sqrt(T)*sqrt(3)
so f'/60=sqrt(3)
or
f'=60*sqrt(3)
=104 Hz

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