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Chapter 14: Problem 25

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 in the main cables of the George Washington Bridge is approximately \(v \approx 3925.07 \mathrm{m/s}\).

Step by step solution

01

Identify given values

First, identify the relevant values given in the problem. The mass per unit length (渭) is given as \(4100 \mathrm{kg/m}\) and the tension (T) is given as 250 MN, which is the equivalent of \(250 \times 10^6 \mathrm{N}\).
02

Apply the wave speed formula

Now apply the formula for wave speed. The speed (v) of a transverse wave in a string or cable under tension is given by \(v = \sqrt{T/渭}\). Substituting the given values of T and 渭 into this formula gives: \(v = \sqrt{(250 \times 10^6 \mathrm{N})/(4100 \mathrm{kg/m})}\).
03

Compute the wave speed

Perform the calculation that was set up in the previous step to find the wave speed: \(v = \sqrt{(250 \times 10^6)/(4100)} \mathrm{m/s}\).

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