In a microwave oven, standing electromagnetic waves are established inside a metallic cavity of length \(L\). The metallic walls act as reflective boundaries, forcing the electric field to have nodes at both ends. Food placed inside the cavity experiences maximum heating at the antinodes, which are the points of maximum electric field amplitude. When the microwave operates at a resonant frequency \(f_0\), the distance between adjacent antinodes is \(d_0\). If the operating frequency is increased to \(3f_0\), what is the new distance between adjacent antinodes?