Equal Time Equal Distance Drop

Equipment: Two strings with 6 weights each attached and a Xerox box lid that acts as a sounding board. The weights are 1" diameter red wooden balls. These weights are attached at equal intervals of 50cm on string 1. They are attached at squared intervals (0, 10, 40, 90, 160 and 250cm) on string 2. Both strings are 250cm long.

What it does: 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.

Concepts Demonstrated: The acceleration of falling bodies.

Classroom assembly:

1. Place the sounding board (Xerox box lid) on the floor next to a bench.
2. Stand on the bench.
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.

• 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.

Cautions: Be careful not to fall off the bench.

Setup Time: Short.

Difficulty: Straightforward.

Visibility: High. The sound of impact can be heard throughout a large lecture hall.

Related demonstrations:

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."

Original Construction: Constructed from string and 12 x 1" diameter wooden balls. The balls were painted red for visibility.