Standing wave antinodes from reflector node

Steps:

• Calculate wavelength: λ = c/f = 3×10^8 m/s / 1×10^9 Hz = 0.3 m = 30 cm.
• Distance L = 45 cm; node at reflector (x=0), antinodes at (2n-1)λ/4 from it.
• Antinode positions: λ/4 = 7.5 cm, 3λ/4 = 22.5 cm, 5λ/4 = 37.5 cm (7λ/4 = 52.5 cm > 45 cm).
• Three antinodes lie within 0 to 45 cm.

Why C is correct:

• Standing wave theory places antinodes at odd multiples of λ/4 from a node, yielding exactly three in 45 cm.

Why the others are wrong:

• A: Counts only first antinode, ignores pattern repetition.
• B: Counts up to second antinode, misses third within distance.
• D: Includes position beyond 45 cm.

Final answer: C