Answer to Question #293803 in Physics for Lug

Question #293803

A stretched wire emits a fundamental note of 256Hz keeping the stretching force constant and reducing the length of wire by 10cm, the frequency becomes 310Hz . Calculate the original length of the wire


1
Expert's answer
2022-02-04T07:40:56-0500

How does frequency change with length and how does it depend on tension?


f=12LTμ.f=\dfrac 1{2L}\sqrt\dfrac{T}{\mu}.


For the condition given, we have


f1=12L1Tμ, f2=12L2Tμ, f1f2=L2L1, f1f2=(L110)L1, L1=10f2f2f1=57 cm.f_1=\dfrac 1{2L_1}\sqrt\dfrac{T}{\mu},\\\space\\ f_2=\dfrac 1{2L_2}\sqrt\dfrac{T}{\mu},\\\space\\ \dfrac {f_1}{f_2}=\dfrac{L_2}{L_1},\\\space\\ \dfrac {f_1}{f_2}=\dfrac{(L_1-10)}{L_1},\\\space\\ L_1=\dfrac{10f_2}{f_2-f_1}=57\text{ cm}.


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