Collegetown bridge puzzle (Jim Papadopoulos, 1986). Photo of bridge.

Rules: Prize for first correct response = free cup of coffee or equivalent. Submit solutions to Andy Ruina (ruina@cornell.edu). No fair if you learned the answer from another person or course (like Engr 116, etc.).

Setup: Walk across the pedestrian bridge that connects C-town bagels and Bard-Thurston-Kimball. Using a pocket knife or similar metal object, tap the middle face of one of the square top tubes (the hand rails). Tap the tube over and over as you walk from one end to the other. Listen to the pitch of the ring you hear and how it changes.

puzzle: What is the reason for the pattern of pitches you hear? Your answer should be justified, in part, by methods you have learned recently in TAM 202.

The winning solution by a 202 student

The bridge has three distinct resonance
frequencies, the lowest at the outside, and the highest near the center of
the bridge. It also has slight variations where the joints are, but this is
just due to the joints.
1 2 3 2
1
Bard Hall ---------|---------|---------|---------|--------- C-Town
Bagels
frequency @ 3 > frequency @ 2 > frequency @ 1
In the section between the lowest tone (tone 1) and the middle tone
(tone 2), there is a connector. In the section where tone 2 turns into tone
3, there is no connector but there are, if you look closely, welding marks
where they joined two bars.
The bars, of course, are not solid. My guess is the handrail is made of
5 different bars welded (or connected somehow) together. Why would they do
this? Stress at the center of the bridge is much greater than the stress
near the sides. Therefore, the bars used to support the higher load must be
stronger than the ones supporting less weight. They could be the same, but
this would lead to increased weight and be a general waste of money. The
bar in the center of the bridge is the thickest, followed by the two bars
connected to it, and the end bars are the thinnest. The thicker bars
resonate at a higher frequency than the thin bars due to a restoring force
(ex. tuning forks).

Comments from Ruina

That the "stress at the center of the bridge is much greater than the stress near the sides"
follows from finding the bar forces, by the method of sections say. Just like the for the
top bars in lab 1 or in problem 1 of prelim 1. The cover of prelim 1 shows the bridge.