Went to Bergen today with three students who were hoping to pick up a prize in a science competition. The prize didn't materialise but we did get to visit vilvite which I thought meant wild knowledge but that would be a different spelling, it actually means "will know" and is one of those science parks with loads of activities, like measuring the speed of a football. I managed 30kmh^-1, not very impressive. One exhibit that caught my eye was the oscylinder scope. It's a stretched string in front of a rotating drum which has black and white lines on it. When you pluck the string you see a wave pattern as in the photo. The wave pattern isn't the wave in the string as this would have a much bigger wavelength however it is related. I think its something like a double strobe effect. You only see the string when its over a white band which you only see when the lights are shining. Now the lights are flashing on and off at 100 Hz due to the mains supply, (100 not 50 since they are on  for both direction of current). Explanations I've read on line don't mention the flashing light but I can't see how it would work without (see below for what is probably the correct explanation). If you have one oscillating point in a light that flashes with the same frequency as the oscillation you would see it always at the same place, it appears to stop. What seems to be happening here is that each bit of the string is seen a little after the bit above resulting in the wave pattern. I guess one could calculate the frequency of the sound from the number angular velocity of the drum but I haven't got that far yet. I was thinking of making one until I saw this video on youtube. It seems that taking a video with an iphone produces the same effect.

Now I'm having second thoughts about whether the effect depends on flashing electric lights or not. I'll have to get a student to change their EE topic.

Attempt 2: If viewed from one point the drum will be like a strobe enabling you to see the string every time a white band goes past. If this coincides with the string being in the equilibrium position then that point on the string will appear in the middle. If you now consider the point directly below the white bars will arrive there slightly later so this point will be slightly off the central line. Depending on the speed of the drum there will be a point xcm below the first where the string is again in the equilibrium position when the white band passes. So the time difference between the first point and the second must be half a cycle I think. Maybe I should leave the rest for my students to figure out.

Attempt 3: Now I've definitely got it. Forget that there is a wave in the string and think of the string as just oscillating up and down. As one white stipe moves along the string a bit of the string is seen to oscillate up and down like in the animation below.

You can see that the this gives the appearance of a wave. If this was speeded up and your eyes would retain the image (persistence of vision) and you'd see a sine wave. The wavelength of this wave depends on the speed of the moving window. This is pretty much how an oscilloscope works hence the name oscylinderscope, duhh.