Projects in High-Speed Photography
Supersonic Snap #2
The image below is cropped from a full-size frame (640 x 480 pixels) captured from videotape. A section of meter stick was superimposed on the photo. This section was cut from a frame of the same size and resolution as the snap. The meter stick was filmed in the plane of the towel's motion immediately after the snap was filmed.
The image may be printed out for analysis. Try measuring the distances moved by the tip of towel for each image in succession, starting with the first blue image on the right. (Measurements will become less certain after the 2nd blue image, since the end of the 2nd red image is indistinct and the towel begins to show some fraying at this point.) The towel tip moves along a curved line, so you'll need to sketch out your best guess of its path. Lay out a string or thread along the path that you think the tip would have taken. Then measure the length of the string. The time interval between images was 0.000098 seconds (accurate to within 0.000002 second). Calculate the average speeds (distance ÷ time) between successive images or make a graph of distance traveled versus time. There are significant uncertainties in distance measurement due to the blurring of the towel tip, and these will introduce uncertainty into your speed calculations.
How much greater is the greatest measured speed than the speed of sound (345 m/s)? Is the difference outside the bounds of your measurement uncertainties?