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27 November, 04:44

Two metal rods are made of different elements. The interatomic spring stiffness of element A is 7 times larger than the interatomic spring stiffness for element B. The mass of an atom of element A is 7 times greater than the mass of an atom of element B. The atomic diameters are approximately the same for A and B. What is the ratio of the speed of sound in rod A to the speed of sound in rod B?

A) The ratio of the speed of sound in rod A to the speed of sound in rod B is 0.5.

B) The ratio of the speed of sound in rod A to the speed of sound in rod B is 1.

C) The ratio of the speed of sound in rod A to the speed of sound in rod B is 2.

D) The ratio of the speed of sound in rod A to the speed of sound in rod B is 6.

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  1. 27 November, 04:50
    0
    B) The ratio of the speed of sound in rod A to the speed of sound in rod B is 1.

    Explanation:

    Applying Hooke's law,

    F = - kx

    Where,

    F = force

    k = spring stiffness

    x = length

    Element A

    F/7k = x

    Since, mass = F/A

    Ma = 7Mb

    Therefore,

    7Mb/A*7kb = x

    Mb/A*k = x

    Element B

    F/k = x

    Since, mass = F/A

    Mb = Mb

    Therefore,

    Mb/A*kb = x

    Ratio of mass of element A and element B

    Mb/A*kb : Mb/A*kb

    1 : 1
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