Final answer:
In the described standing wave with 3 antinodes on a 20.30 m long spring, there are 4 nodes. The wavelength of the waves creating this standing wave is 10.15 meters.
Step-by-step explanation:
The student has described a situation where a standing wave has formed on a spring that is 20.30 meters in length with 3 antinodes. Since standing waves on a string or spring have nodes at both fixed ends, and one node in between each pair of antinodes, the total number of nodes N is given by N = A + 1, where A is the number of antinodes. Therefore, with 3 antinodes, there would be 4 nodes (including the nodes at the fixed ends of the spring).
To find the wavelength of the waves causing the standing wave, we use the formula λ = 2L/n, where L is the length of the spring, and n is the number of segments between nodes, which is equal to the number of antinodes plus one or the number of nodes in this case. Therefore, the length of the spring is divided into 4 equal segments by the nodes. With 3 antinodes, the wavelength is thus λ = 2(20.30 m) / 4 = 10.15 m.
This conclusion comes from the basic understanding of standing waves and the relationship between antinodes, nodes, and wavelength on a medium like a spring. Antinodes denote points of maximum amplitude, while nodes are points of zero amplitude, where the medium does not move.