2. Questions Bank
  3. JEE Main & Advanced
  4. Physics
  5. Wave Mechanics

JEE Main & Advanced Physics Wave Mechanics Question Bank Self Evaluation Test - Waves

  • question_answer
    A sonometer wire of length 1.5 m is made of steel. The tension in it produces 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?

    A)  188.5 Hz

    B)  178.2 Hz

    C) 200.5 Hz

    D) 770 Hz

    Correct Answer: B

    Solution :

    [b] Fundamental frequency, \[f=\frac{v}{2\ell }=\frac{1}{2\ell }\sqrt{\frac{T}{\mu }}=\frac{1}{2\ell }\sqrt{\frac{T}{A\rho }}\] \[\,\left[ \because v=\sqrt{\frac{T}{\mu }}\,and\,\mu =\frac{m}{\ell } \right]\] Also, \[Y=\frac{T\ell }{A\Delta \ell }\Rightarrow \frac{T}{A}=\frac{Y\Delta \ell }{\ell }\] \[\Rightarrow \,f=\frac{1}{2\ell }\sqrt{\frac{\gamma \Delta \ell }{\ell \rho }}\]                    ? (i) Putting the value of\[\ell ,\,\frac{\Delta \ell }{\ell }\],\[\rho \]and \[\gamma \] in \[e{{q}^{n}}\]. (i) we get, \[f=\sqrt{\frac{2}{7}}\times \frac{{{10}^{3}}}{3}\] or, \[f\approx 178.2Hz\]


You need to login to perform this action.
You will be redirected in 3 sec spinner