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Chapter 14: Problem 27

The main cables supporting New York's George Washington Bridge have a mass per unit length of \(4100 \mathrm{kg} / \mathrm{m}\) and are under 250-MN tension. At what speed would a transverse wave propagate on these cables?

Short Answer

Expert verified
The speed at which a transverse wave propagate on the support cable is approximately \(7810 \, m/s\).

Step by step solution

01

Identify given parameters

From the problem, we can see that the tension \(T= 250 \times 10^6 \,N\) (converted MN to Newtons), and the mass per unit length, \(\mu= 4100\, kg/m\).
02

Apply the formula for wave speed

The formula for wave speed in terms of tension and mass per unit length is \(v=\sqrt{\frac{T}{\mu}}\). By substituting the aforementioned parameters into the formula we get, \(v=\sqrt{\frac{250 \times 10^6\, N}{4100\, kg/m}}\).
03

Calculation

By doing the calculation, we find that the speed at which a transverse wave would propagate on these cables is \(v \approx 7810 \, m/s\).

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