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The frequency of vibratiorn of a …

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The frequency of vibratiorn of a string depends on the length 'L' between the nodes,the tension 'F' in the string and its mass per unit length 'm'.Guess the expression for its frequency from dimensional analysis

    • Posted by Hemant Yadav 6 years, 6 months ago

    CBSE > Class 11 > Physics
    • 1 answers

    Dhruv Sarkar 6 years, 6 months ago

    Let the frequency be v.Now, v=kL^aF^b(m/l)^c, where k is the constant of proportionality.By taking the dimensions of the LHS and RHS we get, [M^0L^0T^-1]=[L^a][M^bL^bT^-2b][M^cL^-c] [M^0L^0T^-1]=[M^b+cL^a+b-cT^-2b] By equating the powers we get, b=1/2; c=-1/2 and a=-1 Hence by putting the values we get, v=(k/L)×(√F/m)

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