Suppose we have a 42.2 kg mass hanging on a steel wire over a pulley, like in our experiment. We have 0.8 mm diameter wire, made out of carbon steel (mass density ρ = 7860 kg/m3). What is the linear mass density of the wire?
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 frequency of fundamental mode (n=1)?
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 frequency of fundamental mode (n=1)?
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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.
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.