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JEE Main & Advanced Physics Wave Mechanics Question Bank Basics of Mechanical Waves

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    \[{{v}_{1}}\] and \[{{v}_{2}}\] are the velocities of sound at the same temperature in two monoatomic gases of densities \[{{\rho }_{1}}\] and \[{{\rho }_{2}}\] respectively. If \[{{\rho }_{1}}/{{\rho }_{2}}=\frac{1}{4}\] then the ratio of velocities \[{{v}_{1}}\] and \[{{v}_{2}}\] will be  [KCET  2000; AIIMS 2002; AFMC 2002]

    A)            1 : 2                                          

    B)            4 : 1

    C)            2 : 1                                          

    D)            1 : 4

    Correct Answer: C

    Solution :

                At given temperature and pressure                    \[v\propto \frac{1}{\sqrt{\rho }}\]Þ\[\frac{{{v}_{1}}}{{{v}_{2}}}=\sqrt{\frac{{{\rho }_{2}}}{{{\rho }_{1}}}}=\sqrt{\frac{4}{1}}=2:1\]


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