The velocity of a wave on a wire or string is not dependent (to a close approximation) on frequency or amplitude and is given by v2 = T/µ, where T is the tension in the wire and µ is the linear mass density. The linear mass density is the mass per unit length of wire, so that the linear mass density µ is the product of the mass density and the cross-sectional area.
A certain wire A (see figure) has tension 2000 N and a circular cross section of diameter 0.4 mm. A sine wave is traveling to the right with frequency 200 Hz.
Wire B is made of the same material as wire A with half the diameter.
One long, straight wire has a diameter of 0.4 mm made of steel (density 8.0 g/cm3). Another wire has the same tension, made of a synthetic material (density 2.0 g/cm3). What must the diameter of the second wire be in order to have the same wave velocity?