Here's why:
* Fundamental Frequency: This is the lowest frequency at which a string can vibrate. It's also the frequency at which the string vibrates with the largest amplitude.
* Nodes and Antinodes: When a string vibrates at its fundamental frequency, it has two fixed points called nodes at its ends, and one point of maximum displacement in the middle called an antinode.
* Wavelength: The wavelength is the distance between two consecutive points that are in phase (meaning they are moving in the same direction at the same time). In this case, the distance between two consecutive antinodes is one wavelength.
Since the string has one antinode in the middle, the length of the string is equal to half of the wavelength (distance between two antinodes).
Visualizing it:
Imagine a string fixed at both ends. When it vibrates at its fundamental frequency, it looks like a single hill in the middle. The length of this hill is half the distance between two identical hills (wavelength).
