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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

Answer :

Answer:

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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