Final answer:
The velocity of a longitudinal wave in a solid is not determined by the length of the rod, but by the material's properties, including its modulus of elasticity and density. The wave velocity increases with increasing tension for waves on a string, and is not independent of the material.
Step-by-step explanation:
The velocity of a 1-D constrained rod/longitudinal wave is determined by the properties of the material through which the wave is traveling. Specifically, it is not dependent on the length of the rod (A), but rather, it is influenced by the material's properties. The wave velocity is not independent of the material (B) as it depends on the modulus of elasticity and density of the material. Contrary to option (C), the wave velocity decreases with increasing density. Regarding tension, option (D) suggests that wave velocity decreases with increasing tension, which is inaccurate for longitudinal waves in solid materials, as they are not typically characterized by tension. Instead, for waves on a string, the wave velocity increases with increasing tension and decreases with an increase in the linear mass density or the weight of the suspended mass.