Max speed of wave on a string from elastic limit given density

[lizzyb]

How do I set this up? "The elastic limit of a piece of steel wire is 2.7 X 10^9 Pa. What is the maximum speed at which transverse wave pulses can propagate along this wire before this stress is exceeded? (The density of steel is 7.86 X 10^3 kg/m^3)

I know $$v = \sqrt{\frac{T}{\mu}}$$ so I guess I'd solve for T? And how do I pull the force from the elastic limit without the area?

thanx!

 

[nrqed]

How do I set this up? "The elastic limit of a piece of steel wire is 2.7 X 10^9 Pa. What is the maximum speed at which transverse wave pulses can propagate along this wire before this stress is exceeded? (The density of steel is 7.86 X 10^3 kg/m^3)

I know $$v = \sqrt{\frac{T}{\mu}}$$ so I guess I'd solve for T? And how do I pull the force from the elastic limit without the area?

thanx!

Hi.

Notice that $\rho = { mass \over length \times area}$ and $\mu = {mass \over length}$ so that $\rho = {\mu \over area}$ where, by "area" I mean the cross sectional area.

Also, Pressure = Force over area, so $P_{max} = {T_{max} \over area}$. With this you should be able to rewrite the speed in terms of the pressure and the volume mass density $\rho$.

I hope this helps

Patrick

 

[lizzyb]

yes it helped! i hope i remember it! thanks!