Final answer:
The position of the nodes from the ends in a string vibrating in its third harmonic is 0.5 meters. The nodes are located at positions of 0.5m, 1.0m, and 1.5m from one end.
Step-by-step explanation:
The question is about determining the position of the nodes in the third harmonic of a string's vibration. In the third harmonic, there are three segments of the string that are vibrating, meaning there are four nodes including the two fixed ends. Since the distance between the extreme end nodes is given as 2 meters, we can determine the node positions by dividing the string into equal segments corresponding to the number of node intervals for the third harmonic, which is 3 intervals.
To find the position of the nodes from the ends, we divide the total distance by the number of intervals:
Position of nodes from the ends = Total distance / (Number of intervals + 1)
Position of nodes from the ends = 2m / 4
Position of nodes from the ends = 0.5m.
Therefore, the answer to the question is 0.50m, and the nodes are located at 0.5m, 1.0m, and 1.5m from one end of the string.