A long slender bar is made from an unknown material. The...

A long slender bar is made from an unknown material. The length of the bar is $0.83 \mathrm{~m}$, its cross-sectional area is $1.3 \times 10^{-4} \mathrm{~m}^{2}$, and its mass is $2.1 \mathrm{~kg}$. A sound wave travels from one end of the bar to the other end in $1.9 \times 10^{-4} \mathrm{~s}$. From which one of the materials listed in Table $10.1$ is the bar most likely to be made?

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Density

Density is the mass per unit volume of a material and is computed by dividing mass by volume. It plays a crucial role in determining how a material responds to forces and is used in calculations involving the behavior of waves within the material, such as the speed of sound. A lower density generally leads to faster wave propagation if the material’s stiffness remains high.

Young's Modulus

Young's modulus is a measure of the stiffness of a material, representing the ratio of stress to strain within the elastic limit. It quantifies how much a material deforms under a given load. In the context of sound waves, a higher Young's modulus indicates that the material is stiffer, contributing to a higher speed of sound through the relation v = sqrt(E/?).

Speed of Sound in Solids

The speed of sound in a solid is determined by the material's stiffness (Young's modulus) and its density, following the relation v = sqrt(E/?). This concept is fundamental in material science as it connects mechanical properties with wave propagation, providing insights into the material's elastic behavior and aiding in material identification based on observed wave speeds.

Transcript

Please give Ace some feedback