Question

A spring is 20.30 m long. a standing wave on this spring has 3 antinodes. Draw a picture of this standing wave (yes, actually draw this picture). How many nodes does this standing wave have? What is the wavelength of the waves that are traveling on this spring to create this standing wave?

Answer 1

In a spring that is 20.30 m long with three antinodes, there would be four nodes, and the wavelength of the wave creating the standing wave is 10.15 m.

Step-by-step explanation:

The question pertains to the concept of standing waves in physics, which are waves trapped in a medium between two fixed points, such as a spring or string. With three antinodes, the wave pattern would have more nodes, specifically four, because a node occurs at each end and between each antinode. Given that the spring is 20.30 m long, the wavelength (λ) can be determined by noting that two antinodes encompass one full wavelength. Therefore, since we have three antinodes and two gaps between them, the wavelength is half the length of the spring, or λ = 20.30 m / 2 = 10.15 m.

Answer 2

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.