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05.02.2020 •
Mathematics
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 rho3. if y1 > y2 > y3 and if rho1 < rho2 < rho3, which material has the highest speed of sound? group of answer choices
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Ответ:
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
Ответ: