Final answer:
Increasing the thickness of a string increases its linear mass density. The wave speed on a string depends on both its tension and linear mass density. Doubling the tension results in an increased wave speed, assuming constant linear mass density.
Step-by-step explanation:
The physical quantity that is increased by increasing the thickness of the string is the linear mass density of the string. When we refer to a string's thickness in a physical context, we're often discussing its linear mass density, which is the mass per unit length of the string. Enhancing the string's thickness means more material per unit length, and thereby an increased linear mass density. With respect to waves on a string, the speed of a wave is determined by both the tension in the string and its linear mass density. If the tension is doubled, while keeping the linear mass density constant, the speed of the waves on the string will increase, following the relationship that wave speed is proportional to the square root of the tension divided by the linear mass density.
Further exploration into the property of strings under tension reveals that a string's resistance to deformation (represented by the proportionality constant k) is affected by its thickness. Thicker strings, such as thicker nylon strings or steel strings, typically stretch less for the same applied force, indicating a larger value of k. This parameter influences how a string behaves under tension but is slightly different from the linear mass density, which directly influences wave speed.