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JEE Main & Advanced AIEEE Solved Paper-2013

  • question_answer
    A sonometer wire of length 1.5 m is made of steel. The tension in it produce an elastic strain of 1%. What is the fundamental frequency of steel if density and elasticity of steel are \[7.7\times {{10}^{3}}kg/{{m}^{3}}\] and \[2.2\times {{10}^{11}}\] \[N/{{m}^{2}}\]respectively?     AIEEE Solevd Paper-2013

    A) 188.5 Hz                              

    B) 178.2 Hz              

    C)        200.5 Hz              

    D)        770 Hz

    Correct Answer: B

    Solution :

    Stress \[=Y\times \frac{1}{100}=2.2\times {{10}^{9}}\] \[V=\sqrt{\frac{T}{\mu }}=\sqrt{\frac{T}{\frac{M}{L}}}=\sqrt{\frac{\frac{T}{{{L}^{2}}}}{\frac{M}{{{L}^{3}}}}}=\sqrt{\frac{stress}{density}}\] \[=\sqrt{\frac{2.2\times {{10}^{9}}}{7.7\times {{10}^{3}}}}=\sqrt{\frac{2}{7}}\times {{10}^{3}}\] \[V=\frac{V}{2\ell }=\sqrt{\frac{2\times {{10}^{3}}}{72\times 1.5}}-=178.2\,Hz\]


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