- #1
bcjochim07
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Homework Statement
The frequency of a standing wave on a string is f when the string's tnesion is T. If the tension is changed by the small amount deltaT, witout changing the length, show tat the frequency changes by an amount deltaf, such that
deltaf/f = .5 * deltaT/T
Homework Equations
The Attempt at a Solution
v=sqrt(T/Mu)
f= (1/lambda)*sqrt(T/Mu) When tension is increased, the wavelength will still be the same
f+deltaf=(1/lambda)*sqrt((T+deltaT)/Mu)
so delta f=(1/lambda)*sqrt((T+deltaT)/Mu)-f
deltaf/f = [(1/lambda)*sqrt((T+deltaT)/Mu)-f]/((1/lambda)*sqrt(T/Mu))
deltaf/f = sqrt(T+deltaT)/sqrt(T) -1
But I can't get it simplified any more than this