What is linear mass density?
Linear mass density is the amount of mass per unit length.
Just as ordinary density is mass per unit volume, linear density is mass per unit length. Linear densities are usually used for long thin objects such as strings for musical instruments.
Suppose we have a 0.80 mm diameter guitar string made of carbon steel (density = 7.860 g/cm³). What is the linear mass density of the string?
Step 1: Find the volume of a length (say, 1 m = 100 cm) of the string.
The radius of the string is half the diameter.
Step 2: Find the mass of the wire.
Step 3: Find the linear mass density.
Linear mass density =
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