Stationary Wave Node Separation

Steps:

• In a stationary wave, distance between adjacent nodes is λ/2, where λ is the wavelength of the progressive waves.
• Given node separation of 1.5 m, λ/2 = 1.5 m, so λ = 3 m.
• Frequency f = 300 Hz.
• Wave speed v = f λ = 300 × 3 = 900 m/s.

Why D is correct:

• Speed v = f λ follows the wave equation, with λ = 2 × node separation = 3 m, yielding 900 m/s.

Why the others are wrong:

• A: 100 m/s gives λ = 100/300 ≈ 0.33 m, node separation ≈ 0.17 m (too small).
• B: 200 m/s gives λ ≈ 0.67 m, node separation ≈ 0.33 m (too small).
• C: 450 m/s gives λ = 1.5 m, node separation = 0.75 m (half of 1.5 m).

Final answer: D