Steel piano string the lowest note on a grand piano has a, Ask an Expert

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Steel Piano string
The lowest note on a grand piano has a frequency of 27.5 Hz. The string is 2 m (more or less; let's just assume it is exactly 2.000 m) long, and its tension is 1000 N (again, more or less, so let's say it's exactly 1000 N).

1. What must the length density ? (mass per unit length, in units of kg/m or g/m) of the string be?
2. If the string is to be made of steel, which has a volume density ? = 7800 kg/m^3, what must the diameter of the string be?

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