1C20.20 Equal Time Equal Distance Drop

Concepts

Acceleration of falling bodies

Overview

When the strings are dropped, the weights hit the ground one by one and the resulting impact is heard. Because of the acceleration due to gravity, the time between sounds for the equally spaced weights grows shorter, while the time between sounds for the squared interval weights remains constant. Note: despite the small size of the string, the sound of impact can be heard throughout a large lecture hall.

Details

Equipment

  • [1] String with 6 weights attached at equal intervals of 50 cm
  • [1] String with 6 weights attached at squared intervals (0, 10, 40, 90, 160 and 250 cm)
  • [1] Xerox box lid
  • [1] Ladder

Classroom Assembly

  1. Set up the ladder on a clear, open area.

Important Notes

  • Be careful not to fall off the ladder.

Script

  1. Place the sounding board (Xerox box lid) on the floor next to the ladder
  2. Stand on the ladder.
  3. Hold the string with equally spaced weights so the bottom weight is just above the sounding board.
  4. Drop the string. Impacts will be heard at 0, 0.32, 0.45, 0.55, 0.64 and 0.71 seconds after dropping. Students should be able to hear the time interval grow shorter. Repeat to allow the students to train their ears to hear the decreasing interval between impacts. Discuss the resulting sound pattern.
  5. Repeat the process with the squared interval weights. Here the impacts are equally spaced and .14 seconds apart. Discuss the resulting sound pattern.
Variations: Meiners (see references below) suggests using a microphone and an oscilloscope. Edge suggests shifting the position of one of the weights to demonstrate the sensitivity of the ear to non-uniform intervals. According to him 20% is easily detectable.

 

Additional Resources

References

  • PIRA 1C20.20
  • Video Encyclopedia 01-12
  • Sutton M-84; Meiners 7-1.12; DHP Mb-12; DaR M-094; String and Sticky Tape 1.22 (from TPT 16(4), 233 (April 1978)); Rogers "Physics for the Inquiring Mind" Problem 22, p24; Joseph ea "Sourcebook" p369; Taylor 1.22 p46; Miller p22. To quote Taylor: "Although very rapid, the human ear-brain system can detect the time intervals and it is abundantly clear that the time intervals become shorter as the weights that started off higher reach the floor."

Disclaimer

  • Don't attempt this at home!

Last revised

  • 2018

Technicals

  • Original construction: made from string and 12 x 1" diameter wooden balls. The balls were painted red for visibility. Both strings are 250 cm long.

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If you have any questions about the demos or notes you would like to add to this page, contact Ricky Chu at ricky_chu AT sfu DOT ca.