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.)