Two pieces of string are identical except one piece is twice the length of the other. Each is tied to a rigid support at one end, stretched taut, and subjected to the same sudden jerk at the unattached end. What do you predict will happen? Justify answer.

Based on the given information, we can predict that the shorter piece of string will experience a greater displacement than the longer piece of string when subjected to the same sudden jerk. This prediction can be justified using the principle of wave propagation.

When a sudden jerk is applied to the unattached end of the strings, it generates a wave that travels through the length of the string until it reaches the rigid support at the other end. The speed of wave propagation is determined by the tension and linear density of the string.

In this scenario, both pieces of string are identical except for their lengths. Assuming they have the same linear density, the shorter string will have less total mass compared to the longer string. As a result, the tension in the shorter string will be lower than in the longer string due to the same sudden jerk force being divided across a smaller mass.

According to the wave equation, the speed of wave propagation is inversely proportional to the square root of the tension and directly proportional to the square root of the linear density. Therefore, the shorter string will have a lower wave speed compared to the longer string.

Since the wave speed is lower in the shorter string, the wave will take longer to reach the rigid support compared to the longer string. As a result, the displacement of the shorter string will be greater than the displacement of the longer string because the wave will not have fully propagated through the shorter string by the time it reaches the support.

In conclusion, when subjected to the same sudden jerk, the shorter piece of string will experience a greater displacement than the longer piece of string due to the difference in their lengths and the resulting difference in wave propagation speeds.