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Chapter 14: Problem 28

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 of a transverse wave on these cables would be approximately \(1522 \, m/s\).

Step by step solution

01

List the given values

The problem gives us the tension \(T = 250 \times 10^{6} \, N\) (we converted MN to N) and the mass per unit length \(\mu = 4100 \, kg/m\).
02

Substitute into formula

Substitute these values into the wave speed formula \(v = \sqrt{T/\mu}\). This gives \(v = \sqrt{\frac{250 \times 10^{6} \, N}{4100 \, kg/m}}\). The units N and kg/m in the square root naturally combine to give m/s, which is the correct unit for speed.
03

Perform the calculation

Extract the square root and complete the division to find the wave speed \(v\).

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