Physics: Would sound travel faster in a thick piece of metal (high density) or a large hollow piece of metal (low density)?

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Would sound travel faster in a thick piece of metal

cornpops4037

22.01.2022

See the explanation below

Explanation:

The speed of sound waves can be calculated using the following equation:

$v_{s}=\sqrt{\frac{E}{ro} } \\where:\\E = Young's modulus [GPa]\\ro = density of the material [kg/m^3]$

Let's do the exercise of comparing two materials one denser than the other, as is steel and aluminum

ro_steel = 7500 [kg/m^3]

ro_aluminum = 2700 [kg/m^3]

E_steel = 200 [GPa]

E_aluminum = 70 [GPa]

Now replacing the values in the equation for each material.

$v_{steel}=\sqrt{\frac{200*10^9}{7500}}\\ v_{steel}=5163[m/s]$

And for the aluminum

$v_{aluminum}=\sqrt{\frac{70*10^9}{2700} }\\ v_{aluminum}=5091.75[m/s]$

In this way we can see that sound propagates faster in denser materials.

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