Final answer:
The wavelength of a standing wave with five antinodes on a 1-meter long wire is 0.5 meters, calculated by using the relationship between the length of the wire and the number of half-wavelength segments formed by nodes and antinodes.
Step-by-step explanation:
When a 1-meter long wire is plucked to form a standing wave with five antinodes, the pattern is indicative of how the waves interfere and set up a pattern of nodes (points of no displacement) and antinodes (points of maximum displacement).
For such a standing wave, the wavelength (λ) can be determined by considering that there will be a node at each end of the string and a series of antinodes and nodes between them.
Since five antinodes indicate the presence of four full segments each comprising one node and one antinode, this means there are four half-wavelengths (λ/2) in the total length of the string. Hence, the wavelength of the standing wave is twice the length divided by the number of segments.
λ = 2 * Length / Number of half-wavelength segments
λ = 2 * 1m / 4
λ = 0.5m
The wavelength of the standing wave on the string is therefore 0.5 meters.