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JCECE Engineering JCECE Engineering Solved Paper-2014

  • question_answer
    Two cars are moving on two perpendicular roads towards a crossing with uniform speeds of\[72\,\,km/h\]\[\text{and}\]\[36\,\,km/h\]. If first car blows horn of frequency\[280\,\,Hz\], then the frequency of horn heard by the driver of second car when line joining the car makes angle of \[{{45}^{o}}\] with the roads, will.be

    A) \[321\,\,Hz\]                     

    B) \[296\,\,Hz\]

    C) \[289\,\,Hz\]                     

    D)  \[280\,\,Hz\]

    Correct Answer: A

    Solution :

    The component of velocity of source along line joining                 \[{{v}_{s}}={{v}_{1}}\cos {{45}^{o}}=36\times \frac{1}{\sqrt{2}}\] Component of velocity of observer along line joining                 \[{{v}_{0}}={{v}_{2}}\cos {{45}^{o}}\]                 \[=72\times \frac{1}{\sqrt{2}}\]                 \[=10\sqrt{2}\] The frequency of horn                 \[n'=\frac{v+{{v}_{0}}}{v-{{v}_{s}}}\]                 \[n=\frac{330+10\sqrt{2}}{330-5\sqrt{2}}\times 280\]                 \[=\frac{344}{323}\times 280=298\,\,Hz\]


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