# A steel wire in a piano has a length of 0.7 m and a mass of 0.0043 kg. To what tension must this wire be stretched so that the fundamental vibration with frequency of 261.6 Hz?

##T=823.9″N”##

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A steel wire in a piano has a length of 0.7 m and a mass of 0.0043 kg. To what tension must this wire be stretched so that the fundamental vibration with frequency of 261.6 Hz?
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For the fundamental frequency:

##f=(1)/(2L)sqrt((T)/(m))##

##L## = length

##T## = tension

##m## = mass per unit length.

##sqrt((T)/(m))=2Lf##

##T/m=4L^2f^2##

##T=4L^2f^2m##

##T=4xx0.7^2xx261.6^2xx0.0043/0.7##

##T=823.9″N”##

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