Answer :
Final answer:
The ratio of mass per unit length of the A and G strings on the violin is approximately 3.3.
Explanation:
To determine the ratio of mass per unit length of the strings A and G, we can use the formula for wave speed on a string:
Wave speed (v) = sqrt(Tension (F) / linear mass density (μ))
For the A string, the wave speed (vA) is 288 m/s and the tension (FA) is 350 N. For the G string, the wave speed (vG) is 128 m/s and the tension (FG) is 110 N. We can set up equations to find the linear mass density of each string:
vA = sqrt(FA / μA)
vG = sqrt(FG / μG)
Simplifying the equations, we get:
μA = FA / (vA)2
μG = FG / (vG)2
Substituting the given values, we find:
μA = 350 N / (288 m/s)2
μG = 110 N / (128 m/s)2
Calculating these expressions, we find that the ratio of mass per unit length of the strings (A/G) is approximately 3.3.
