The heaviest and lightest strings on a certain violin have linear densities of 2.8 g/m and 0.41 g/m, respectively. What is the ratio of the diameter of the heaviest string to that of the lightest string, assuming that the strings are of the same material?

The ratio of the diameter of the heaviest string to that of the lightest string is approximately √((mass_heaviest / (mass_lightest)) * (0.41 / 2.8)).

Explanation:

To calculate the ratio of the diameters of the heaviest and lightest strings, we can use the formula:

diameter = √((mass / (π * linear density)) * 4)

Let's calculate the diameter of the heaviest string:

diameter_heaviest = √((mass_heaviest / (π * linear density_heaviest)) * 4)

Substituting the given values:

diameter_heaviest = √((mass_heaviest / (π * 2.8)) * 4)

Similarly, let's calculate the diameter of the lightest string:

diameter_lightest = √((mass_lightest / (π * linear density_lightest)) * 4)

Substituting the given values:

diameter_lightest = √((mass_lightest / (π * 0.41)) * 4)

Now, we can calculate the ratio of the diameters:

ratio = diameter_heaviest / diameter_lightest

Let's substitute the calculated values:

ratio = (diameter_heaviest) / (diameter_lightest)

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