1. Wanna hear a weird but true story? (I have a few minutes to type, so here goes). I almost lost my hearing from the lid on the tank of a toilet. Noise-Induced Hearing Loss. You wouldn't think a toilet lid could be so loud, would you? Well, I learned otherwise...
2. I was fixing the mechanism inside the tank of the toilet. The only thing left to do was to put the ceramic lid back on the tank. Unfortunately it slipped out of my hands and banged on the ceramic of the toilet rim. Again, you wouldn't think that would be so loud, would you?
3. Well, the sound stunned me. I stumbled out of the bathroom and fell to my knees in the living room, wondering what had just happened. Did something happen, or did I imagine it? It was surreal. Then I got the idea to test my hearing, because I noticed something seemed weird.
4. I said (in my Space Shuttle comm systems test voice), "Commcheck 1,2,3,...3,2,1". My voice sounded (to me) like I was talking through a kazoo. It was freaky. I tried humming up the scale, and I noticed the kazoo sound was mainly at specific frequencies with regular spacing.
5. The stupid toilet bowl lid only fell about 8 inches. How could it damage my hearing so badly? I looked up the speed of sound in ceramic, divided by the length of the toilet bowl lid (and divided by 2 since the fundamental vibration is a half wavelength). This predicts 3.5 kHz.
6. This frequency is in the audible range. Using the short dimension of the toilet bowl predicts another (higher) frequency. The toilet bowl lid probably resonated at both those frequencies and their harmonics, putting all the energy into just those specific wavelengths.
7. The toilet bowl lid was not chipped or damaged, so the impact energy went mainly into sound (& internal heat) Maybe like half the impact energy went into sound energy. This lid was concave up like an antenna, near my face when it hit, focusing the energy into my face.
8. The energy travels into your inner ear and the cochlea. The pressure wave is strongest at some distance down the cochlea depending on frequency. Since the toilet bowl lid put all the energy into SPECIFIC FREQUENCIES, it was concentrated onto specific spots in the cochlea.
9. Apparently, this concentration of energy was enough to damage the hairs -- to bend them over like trampled grass -- and I was concerned it could be permanent. My hearing was only slightly better the next morning. It was like everybody was still talking at me through kazoos.
10. An audiologist friend told me to go to an ENT physician if not better by 48 hours or the damage could be permanent. Much longer than that and it would be too late to try any of the interventions. Fortunately it got better, right at 48 hours after the event.
11. When I managed the NASA KSC Swamp Works lab, I was responsible for lab safety including hearing protection. I would've never guessed dropping a toilet bowl lid a mere 8 inches could potentially ruin your hearing.
12. I did calculations on the sound level from a toilet bowl lid dropped 8 inches. If it doesn't chip or crack, & it hits such a stiff surface (like the porcelain rim) that it bounces in 1/20th second (IMO reasonable in this case), then from 50 cm away the brief sound is 138 dB.
13. This is just conservation of energy. The initial potential energy was mass times height times gravity. Divide by the 1/20th second that it "rings" out the pressure waves (the sound), and that is acoustic power. Divide by surface area of the toilet bowl lid to get energy flux.
14. Then account for distance to my ears (50 cm) which spread the sound over a larger spherical surface proportional to distance-squared. I divided by 2 assuming 1/2 the energy dissipated as heat inside the ceramic, times a factor of 2 focusing because the lid was dish-shaped up.
15. You have to use an equation to put this number into standard form according to convention: en.wikipedia.org/wiki/Sound_pow…. This predicts 138 dB of sound. Permanent hearing loss from a brief sound occurs at ~140 dB (+/-), so it actually turned out to be in the dangerous zone.
16. But as I said before, all this sound would have been concentrated into narrow bands of frequency determined by resonances of the ceramic material, and I think this makes it far worse for your ears than a broad-band noise of the same power level.
17/18. What makes it dangerous (IMO), is the stiffness of the surface it bounced off, so the energy was converted into sound in a very brief time making it very intense, and the fact that it didn't break or chip so more energy went into sound instead of breaking molecular bonds.
18/18. A safer toilet bowl lid (!) should bust apart on impact, using up the energy by breaking molecular bonds. Or it should be a material that isn't so stiff, so it doesn't resonate at narrow bands of high-pitched frequencies. But there are bigger problems to solve in life! :)
