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Home Experiment – Impact Speed and Sound Level

A while ago I got my hands on a sound level meter and pondered what to do with it. Sound level versus distance from source? Too boring, there’s already a formula for that (see here: Intensity: How Much Power Will Burst Your Eardrums?). What I noticed though is that I’ve never seen a formula relating impact height or speed to sound level, that seemed interesting. So I bought a small wooden sphere at a local store and dropped it from various heights, at each impact recording the maximum sound level. I dropped the sphere from 8 different heights and to reduce the effect of random fluctuations 20 times from each height. So in total I collected 160 data points. I’m not so sure if my neighbors were happy about that.

I calculated the impact speed v from the drop height h using the common v = sqrt (2 * g * h). As you might know, this formula neglects air resistance. However, I’m not concerned about that. The wooden sphere was small and massive and only dropped from heights below about 1 ft. The computed impact speed shouldn’t be off by more than a few percent.

Here’s the resulting plot of impact speed versus sound level (in decibels):

Impact Speed Sound Level Decibel

The fit turned out to be fantastic and implies that if you increase the impact speed by a factor of five, the sound level doubles. What’s the point of this? I don’t know, but it’s a neat graph and that’s good enough for me.

World Population – Is Mankind’s Explosive Growth Ending?

According to the World Population Clock there are currently about 7.191 billion people alive. This year there have been 118 million births (or 264 per minute) and 49 million deaths (or 110 per minute), resulting in a net growth of 69 million people. Where will this end? Nobody can say for sure. But what we can be certain about is that the explosive growth has been slowing down for the past 40 years. I’ll let the graphs tell the story.

Here is how the world population has developed since the year 1700. The numbers come from the United Nations Department of Economic and Social Affairs. From looking at the graph, no slowdown is visible:

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However, another graph reveals that there’s more to the story. I had the computer calculate the percentage changes from one decade to the next. From 1960 to 1970 the world population grew by 22 %. This was the peak so far. After that, the growth rate continuously declined. The percentage change from 2000 to 2010 was “only” 12 %.

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Of course it’s too early to conclude that this is the end of mankind’s explosive growth. There have been longer periods of slowing growth before (see around 1750 and 1850). But the data does raise this question.

Talk to me again when it’s 2020 or 2030.

Just by the way: according to estimates, about 108 billion people have been born since the beginning of mankind (see here). This implies that about 101 billion people have died so far and that of all those born, 6.5 % percent are alive today.

Did somebody say dust in the wind?

More Pirates, Less Global Warming … wait, what?

An interesting correlation was found by the parody religion FSM (Flying Spaghetti Monster). Deducting causation here would be madness. Over the 18th and 19th century, piracy, the one with the boats, not the one with the files and the sharing, slowly died out. At the same time, possibly within a natural trend and / or for reasons of increased industrial activity, the global temperature started increasing. If you plot the number of pirates and the global temperature in a coordinate system, you find a relatively strong correlation between the two. The more pirates there are, the colder the planet is. Here’s the corresponding formula and graph:

 T = 16 – 0.05 · P0.33

 Statistical Snacks_html_40452f20

with T being the average global temperature and P the number of pirates. Given enough pirates (about 3.3 million to be specific), we could even freeze Earth. But of course nobody in the right mind would see causality at work here, rather we have two processes, the disappearance of piracy and global warming, that happened to occur at the same time. So you shouldn’t be too surprised that the recent rise of piracy in Somalia didn’t do anything to stop global warming.