Top: Helmholtz resonance over a bottle (Photo Credit: Youtube.com; Nick Moore/Nik282K)
Bottom: Automotive airflow diagram (Photo Credit: hitechcae.com)
Most people have probably had the experience of driving in a car on the freeway and rolling down their window only to end up with an awful buffeting sound that hurts their ears. People familiar with this phenomenon often refer to it as “side window buffeting”; but in fact, this phenomena is actually caused by something known as Helmholtz Resonance. With that, let’s jump right into it!
As air flows over your car, it decreases the pressure in the flow due to what’s known as Bernoulli’s Principle; that is, in the absence of energy input and losses (which we will assume to be zero for this simple exercise in thought), if the flow is assumed to be incompressible (valid for the relatively low car speed), inviscid (negligible friction, as follows from our assumption of no losses), and steady (not changing with time), then if we assume that the change in elevation is negligible (perfectly valid for air, which is not very dense, over the 5 feet or so from the top to the bottom of your car), we can ascertain that if the velocity of a streamline increases, the pressure decreases, and vice versa.
Inverse relationship between velocity and pressure; flow acceleration and deceleration due to flow area change. Photo Credit: wwk.in
Now, let’s roll down a window while we are travelling on the freeway at elevated speeds. Remember, since we are moving, the pressure of the flow is lower than that of the ambient air far removed from the vehicle (outside the boundary layer); however, the air inside our car is essentially atmospheric pressure (i.e. the standard pressure of the atmosphere, no lower, no higher, just like the ambient air far removed from the vehicle), or perhaps even a little bit higher than atmospheric due to the pressurization from your air conditioning. So now we have the window open with a low pressure flow outside the car and a higher pressure inside the car.
The higher pressure air inside the car wants to go to the lower pressure region, so it is pulled out of the car. Now, we might expect that once enough air flows out to equalize the pressure, the flow will normalize and stop pulling from the car, but this is not the case; the air flowing out of the car has both mass and velocity, the two implicit components of momentum. Thus the air flowing out of the car has momentum and overshoots the equalization pressure, essentially giving away too much pressure from the inside of the car and thus leaving the car’s contents at a lower pressure now than the flow outside the car (creating an effective vacuum). Now the flow outside wants to move inside, but this flow has momentum as well and so it overshoots the equalization pressure and leaves the inside of the car over-pressured. As you might expect, this process can continue, with the flow moving back in forth across the window opening, getting larger and larger, until eventually the damping characteristics of the air itself keep the amplitude of this oscillation from increasing further, thus leading to a steady state oscillation of sorts.
Oscillation amplitude increase due to resonance. Photo Credit: AfifTabsh.com
This oscillation or flow buffeting is exactly what you are hearing, because as the flow buffets, it produces moving pressure waves with it, which our ears pick up as sound. Not only can this buffeting sound be very irritating, but it can also be damaging to your ear drums (which are in effect membranes that effectively convert vibration from pressure waves into sound); this can be especially true if you happen to be driving at the speed that maximizes the system resonance (which results in this Helmholtz Resonance). To better understand this, imagine pushing someone on a swing, if you push them and let go, they oscillate about the vertical swing position until the action of gravity, drag, and frictional losses brings the swing to rest. Now if you give them another push while they are moving backwards towards you, they will continue to swing, but not as fast or high as they could have because you pushed them before they got to the top of the arc. This time, you wait for them to get to the top of the arc (as far back towards you as they travel), and just as they have switch directions (and start swinging forward), you give them a big push. This time, you have added to the energy without cutting short their motion; if you continue to do this, they will swing higher and faster each time. Back to the car, if you are moving with the right speed, the air flowing into or out of the car from the next (upstream) batch of air can synchronize with the pressure osciallation already in place, leading to an increase in the oscillation amplitude (increasing the effective strength of the flow buffeting pressure); this is what happens when the buffeting gets really loud, to the point that it hurts your ears. Moreover, the pressure buffeting in and out of the window disrupts the airflow around the car, leading to vortex shedding, as can be seen in the video linked to here). So what can you do to stop this?
Well, you could slow down in order to avoid the resonance, or speed up for that matter (but not only could you reach another, higher resonant point, but you could also get a speeding ticket, which is no good). You could also roll down your window more or roll it up less (a larger opening will provide a deeper/lower pitch sound and a smaller opening will provide a higher pitch sound) or roll down other windows to relieve the pressure in the car [interestingly, rolling down the opposite, diagonal window usually provides more relief due to the direction of the airflow (rearwards due to the car’s motion and across due to the motion of the buffeting) , i.e. the back right window if the front left one is already down]. Another interesting option is that some cars (like the Chevy Volt) now come with so-called “window air deflectors” that re-route the air further from the window without messing up the car aerodynamics too much, as they deflect the air at an angle that allows it to rejoin the car immediately after the windows.
Chevy Volt window air deflector (lower right corner of the picture). Photo Credit: thecarconnection.com
It should be noted, however, that “side window buffeting” is not the only place that you can see Helmholtz resonance; this can also be seen in the old bar trick of making noise by blowing over a bottle (as pictured at the beginning of the post), many musical instruments, in some automotive exhaust systems that aim to change the sound of the exhaust, and even in some silencing applications in which the created noise is used to cancel out unwanted noise through destructive interference (this can be seen in some aircraft engines, automotive mufflers, and even weapon suppressors/silencers, wherein chambers are used just like the cavity inside the car to produce the noise cancelling pressure waves). Lastly, it’s also worth noting that this whole Helmholtz Resonance effect is more apparent on newer cars than old ones mainly due to the fact that newer cars are more streamlined, which is great for reducing drag, but brings the airlow closer to the car, thus inspiring this phenomenon to occur more easily.
Constructive and destructive interference. Photo Credit: animals.howstuffworks.com
Well, I hope everyone learned something today; now you can go tell your friends about the science behind that annoying thumping! Be sure to check back for Ben’s Open Mind post on Sunday and, I almost forgot, sorry for the 1 hour post delay, I am out of town and do not have readily available Wifi.