Question

Energy, and Strings Problem 11.37 Part A Bulk Caloulate the speed of longitudinal waves in a long ooncrete rod. Express your answer to two significant figures and include the appropriate units Meterial E (N/m-) Modulus, Density B (N/m2) (kg/m) Steel 200 × 109 lion, cast 100×109 Copper 110 x 10 Aluminum 70×109 Concrete 20x10s Granite 45 x 10 Water Mercury 140 x 10 7.8 x 10 90 x 10° 7.8 × 103 140 x 10 8.9x10 70 x 10 2.7 10 Value Units 2.3 x 10 45 × 10° 2.7 × 10, 2.0 x 10 1.0x 10 29 x 10 13.6 x 10 Subm Request Answer Part B Calculate the speed of longitudinal waves in mercury Express your answer to two significent figures and include the appropriate units. Value Units Submit Request Answer Part C Calculate the speed of longitudinal waves in water MacBook Air

Answer 1

Part(A):- Velocity of longitudinal wave in concrete is given by-

   $v_{concrete}=\sqrt{\frac{young's-modulus}{density}}$

$\Rightarrow v_{concrete}=\sqrt{\frac{20\times 10^{9}}{2.3\times 10^{3}}}$

$\Rightarrow v_{concrete}=2.9488\times 10^{3}m/s$

$\mathbf{\Rightarrow v_{concrete}=2.9\times 10^{3}m/s}$        (Up to two significant figures )

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Part(B):- Velocity of longitudinal wave in mercury is given by-

$v_{mercury}=\sqrt{\frac{Bulk-modulus}{density}}$

$\Rightarrow v_{mercury}=\sqrt{\frac{29\times 10^{9}}{13.6\times 10^{3}}}$

$\Rightarrow v_{mercury}=1.46\times 10^{3}m/s$

$\mathbf{\Rightarrow v_{mercury}=1.5\times 10^{3}m/s}$     (up to two significant figure)

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Part(C):-Velocity of longitudinal wave in water is given by-

$v_{water}=\sqrt{\frac{Bulk-modulus}{density}}$

$\Rightarrow v_{water}=\sqrt{\frac{2\times 10^{9}}{1\times 10^{3}}}$

$\Rightarrow v_{water}=1.414\times 10^{3}m/s$

$\mathbf{\Rightarrow v_{water}=1.4\times 10^{3}m/s}$ (up to two significant figures)