What is the formula for the speed of sound's dependence on temperature, and what is its common linear approximation?

Step 1: Identify the formula for the speed of sound's dependence on temperature.
The speed of sound in a medium changes with temperature. For many introductory physics problems, especially when specific material properties for solids are not provided, a common linear approximation is used, similar to that for sound in air. This approximation states that the speed of sound increases by approximately $0.6 \text{ m/s}$ for every $1^\circ C$ rise in temperature.

$$v_T = v_0 + \alpha T$$

where $v_T$ is the speed of sound at temperature $T$ (in Celsius), $v_0$ is the speed of sound at $0^\