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A steel wire is heated to 170^(@)C and held between two rigid supports which are 20cm apart. The wire is allowed to cool to a temperature of 29.6^(@)C. If the frequency of the note produced when the wire is plucked at the middle is 100 k, then find the value of k. (The density D of steel is 7.8xx10^(3)kg//m^(3) and for steel alpha=16xx10^(-6)K^(-1) and Y of steel =20xx10^(10)Pa.). |
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Answer» SOLUTION :THERMAL STRESS in the wire `=alphaYDeltaT` Tension in the wire `=alphaYDeltaTpir^(2)` `N=(1)/(2L)sqrt((T)/(pir^(2)D))=(1)/(2L)sqrt((alphaYDeltaT.pir^(2))/(pir^(2)D))=(1)/(2L)sqrt((alphaYDeltaT)/(D))` Putting values `n=600Hz`. In the fundamental mode as the wire is plucked in the MIDDLE. |
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