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Recent changes to the Golden Gate Bridge’s guardrails have created a new soundscape in the Bay Area. Under high winds, the bridge gives off an eerie, otherworldly wail that can be heard even miles away. The new guardrails are substantially thinner than the previous ones, which reduces the wind load the bridge has to endure. But that thinner profile is also what causes the noise, through a well-known phenomena known as vortex shedding.

As air moves past a non-streamlined body, like a cylinder, it forms counter-rotating vortices that peel off the body at a set frequency. Fluid dynamicists use a non-dimensional number, the Strouhal number, to characterize this vortex shedding. For a simple shape like a cylinder, the Strouhal number is relatively constant, so I decided to do a quick and dirty calculation to examine the wind velocities responsible for the sound. (See also my analysis of Star Trek Voyager’s opening sequence.)

I began by collecting several videos with samples of the bridge’s singing (1, 2, 3). Then I used Adobe Audition to analyze the frequency content of the bridge noise. Below is a sample snapshot from a video taken on the bridge’s bike path, right next to the guardrail. The analysis shows three broad, but distinct peaks: a primary peak at 430 Hz, a small harmonic of that frequency at 860 Hz, and a separate, secondary peak centered at 1070 Hz. The broadness of the peaks, along with the competition between the primary and secondary peaks, is probably responsible for the disconcerting, discordant nature of the sound.

Of the other videos I analyzed, a second video from near the bridge also showed the 430 Hz peak, while a video from further away had a dominant frequency of 517 Hz. There’s a lot of uncertainty introduced in not knowing exactly when each video was filmed, but given the agreement between videos 2 and 3, I suspect that video 1’s higher frequency may be caused by interference and modulation as the sound travels.

With the major frequency in hand, I estimated the size of the new guardrail wires as 10mm in diameter. After some tweaking to adjust the Reynolds number and Strouhal numbers, that gave me an estimated wind speed of 21 meters per second, or about 47 miles per hour. That’s right in line with the 43 miles per hour discussed by the news anchors.

What if the guardrails are a little thinner? If the wires are about 7.5 mm in diameter, then it only takes winds at about 15 meters per second (34 miles per hour) to create that 430 Hz note.

Keep in mind that this analysis doesn’t predict the minimum wind speed needed to create the audible noise; all I’m able to do is a back-of-the-envelope calculation of what the likely wind speed was when a video was recorded. Nevertheless, I hope you’ll find it interesting! (Video credit: KPIX CBS News; image credits: vortex shedding – Wikimedia, frequency analysis – N. Sharp; submitted by Christina T.)

1. ##### Frank Gulla June 10, 2020 at 1:30 pm Reply

Nice job and certainly one that will keep engineering and science students busy for the next few years. A great field exercise for these Corona Virus times.

2. ##### Christoph June 12, 2020 at 3:33 am Reply

When comparing to widely available samples of 440 Hz and 432 Hz on Youtube it is clear that the most prominent frequency is very very close to 440 Hz and different from 432 or 430 (just run a Golden gate video and 432 Hz in parallel on your headphones and play around with volume control). So, the bridge has turned into a giant tuning fork… Video 2 also shows periods of 484 Hz (right at the beginning), 396 Hz (e.g. at 1:40), and for a brief moment at the end 352 Hz. Sounds familiar to trombonists – we are hearing harmonics #10, 11, 9 (and 8) of a 44 Hz frequency. The next one we would expect (528 Hz) however sounds somewhat lower from Golden Gate bridge (video 1, at 0:45).

3. ##### Jean Hertzberg June 17, 2020 at 10:42 pm Reply

Now the question is whether the vortex shedding couples with a vibrational mode of the wires. That will depend on the length and tension.

1. ##### Nicole Sharp June 18, 2020 at 7:47 am Reply

True, but IIRC the guardrail wires are somewhat woven, so presumably their effective length is relatively small.

4. ##### Vijay August 3, 2021 at 1:33 pm Reply

I’m curious to know how you estimate the dia if the guardrail wires as 10mm??

1. ##### Nicole Sharp August 5, 2021 at 10:06 am Reply

Just an order of magnitude guess based on the video. That’s why I also did the math for a slightly thinner wire, too.

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