Suppose we have an kg mass hanging on a steel wire over a pulley, like in our ex

Question

Suppose we have an kg mass hanging on a steel wire over a pulley, like in our experiment. We have mm diameter wire, made out of carbon steel (mass density ? = 7860 kg/m3). What is the linear mass density?

The length that is free to vibrate is 64 cm. If plucked or struck, assume you will mostly hear the n=1 standing wave. What is the fundamental mode (n=1) for the string?

If you were standing near the string, what note would you hear? (pick closest one) (http://www.phy.mtu.edu/~suits/notefreqs.html will help)

Explanation / Answer

mass = density x volume mass = 7860 x Pi d^2/4 x L so mass/L = 7860 x Pi x 0.0008^2/4 work it in kg/m for fundamental L = 1/2 lambda so lambda = 64 x 2 cm = 1.28 m velocity of wave = sqrt(force tension/mass per m) = sqrt( 42.2 x 9.8 / answer from first part) f = v / lambda work it out.

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