Question

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

Answer 1

See the explanation below

Step-by-step explanation:

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

`v_(s)=\sqrt{(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{(200*10^9)/(7500)}\\ v_(steel)=5163[m/s]`

And for the aluminum

`v_(aluminum)=\sqrt{(70*10^9)/(2700) }\\ v_(aluminum)=5091.75[m/s]`

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