Propagation Velocity of Transverse Waves

AI Thread Summary
To find the velocity of propagation of transverse waves in a steel wire, the cross-sectional area must first be calculated. The volume mass density of steel is converted to linear mass density by determining the mass of one meter of the wire. The formula for wave speed is applied: Cw = sqrt(Tension/linear mass density). With a tension of 11.29 N and the calculated linear mass density, the velocity can be determined. This method effectively utilizes the relationship between tension, mass density, and wave speed in the wire.
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A steel wire of radius 0.65 mm is subject to a tension of 11.29 N. Steel has a volume mass density of 7800 kg/m3. Find the velocity of propagation of transverse waves on this wire, in m/s.

I found the cross sectional area of the wire but I am not sure where to go from there. I know I need to convert the volume mass density to linear mass density so I can use the formula
Cw=sqrt(Tension/linear mass density).
 
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Find the volume of one meter of the wire, then its mass.
 
Thank You
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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