In my first post, I talked about how the Doppler effect is a shift in the observed frequency of a wave caused by the relative motion of a source and an observer. In this, my first detailed post, I will try to explain how that actually works. As my mom plays tennis, and this blog is ostensibly aimed at her, I'm going to use a rather tortured tennis analogy.

Suppose my mother is using a ball machine to practice her ground strokes. The ball machine spits out a tennis ball every 2 seconds and each ball moves at the same speed. To use some real numbers, a tennis court is about 24 meters long from baseline to baseline, and let's assume that the balls take 2 seconds to go from the machine to my mother standing at the other baseline (or the ball takes 1 second to get to the net, and then another second to get to my mom). Therefore, as my mom hits a ball, the ball machine is in the process of shooting the next one. As my mom continues to practice, she hits a stroke every 2 seconds.

In this video, my mom hits ground strokes every 2 seconds, and the next ball is released as she hits the previous stroke (this is some pretty great animation, huh? Unfortunately, the timing is not quite right, so it's not 2 seconds in real time).

Now, suppose she wanted to work on her volleying and therefore decides to run to the net. She hits a stroke (a nice approach shot, presumably), and then starts sprinting to the net as the ball machine spits out the next ball. assuming she runs really fast (like Usain Bolt), she can make it to the net in 1 second. When she gets there, the next ball from the ball machine will already be there to meet her (remember, the ball takes 1 second to get to the net, so while my mom was running in, the next ball was also heading towards the net). Instead of hitting a ball every 2 seconds, she'll hit this one after only 1 second, because she was moving relative to the ball machine. Then, once she's stationary at the net, she will once more see a ball every 2 seconds. In a sense, this is the Doppler effect. When my mom, the observer, was moving relative to the ball machine, the source, the frequency with which she hit balls changed (from once every 2 seconds to once every second). Then, when she was no longer moving, the frequency returned to its usual value.

In this one, my mom hits a ground stroke and runs to the net, at which point she is confronted with the next ball after only 1 second, instead of the usual 2. This is caused by the relative difference between her speed and the ball machine, or the Doppler effect (again, the timing isn't quite right, but you get the idea).

## Friday, March 6, 2009

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Hugh, as another mother, I think you get an A+. I've tried to understand the Doppler Effect many times and failed--until now! I like the analogy and I only fret a bit when you get to those formulas!

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Mom Simmons

I love the idea of mom's blog, though I must admit once I left the tennis court I found myself tripping through cold dark matter searching for the light. But, imagining the ball and mom moving gracefully in time from back court to net and back again was the perfect way to describe what for me the math didn't and, alas, may never. Wonderful and very cool..Michelle McKenna, Hugh's mom's friend

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