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16 June, 12:32

Material 1 has Young's modulus Y1 and density rho1, material 2 has Young's modulus Y2 and density rho2, and material 3 has Young's modulus Y3 and density rho 3. If Y1 > Y2 > Y3 and if rho1 < rho2 < rho 3, which material has the highest speed of sound? Group of answer choices

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  1. 16 June, 16:10
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    v_s, 1 > v_s, 2 > v_s, 3

    Step-by-step explanation:

    Given:

    - Material 1:

    modulus of elasticity = E_1

    density of material = p_1

    - Material 2:

    modulus of elasticity = E_2

    density of material = p_2

    - Material 3:

    modulus of elasticity = E_3

    density of material = p_3

    - E_1 > E_2 > E_3

    - p_1 < p_2 < p_3

    Find:

    - Which material has highest speed of sound from highest to lowest:

    Solution:

    - The relationship between velocity of sound in a material with its elastic modulus and density is:

    v_s = sqrt (E / p)

    - Since, v_s is proportional to E^0.5 and inversely proportional to p^0.5, then we have:

    E_1 > E_2 > E_3

    E_1^0.5 > E_2^0.5 > E_3^0.5

    and p_1 < p_2 < p_3

    p_1^0.5 < p_2^0.5 < p_3^0.5

    Divide the two: (E_1 / p_1) ^0.5 > (E_1 / p_1) ^0.5 > (E_1 / p_1) ^0.5

    Hence, v_s, 1 > v_s, 2 > v_s, 3
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