For deep-water waves, which relationship holds between velocity C, wavelength L, and period T?

For deep-water waves, which relationship holds between velocity C, wavelength L, and period T?

• A. C = L/T
• B. C = sqrt(gd)
• C. C = gT
• D. C = d/L

Answer: (A)

In deep-water waves, the speed you measure is how far a wave crest moves in one cycle. That distance is the wavelength, L, and the time for one cycle is the period, T, so the phase velocity is C = L/T. This aligns with the deep-water dispersion relation, ω^2 = gk, where ω = 2π/T and k = 2π/L. Dividing ω by k gives C = ω/k = (2π/T) / (2π/L) = L/T. The other expressions don’t describe deep-water wave behavior: sqrt(gd) is the shallow-water speed, C = gT mixes units and isn’t a valid speed for waves, and d/L isn’t a speed.

In deep-water waves, the speed you measure is how far a wave crest moves in one cycle. That distance is the wavelength, L, and the time for one cycle is the period, T, so the phase velocity is C = L/T. This aligns with the deep-water dispersion relation, ω^2 = gk, where ω = 2π/T and k = 2π/L. Dividing ω by k gives C = ω/k = (2π/T) / (2π/L) = L/T. The other expressions don’t describe deep-water wave behavior: sqrt(gd) is the shallow-water speed, C = gT mixes units and isn’t a valid speed for waves, and d/L isn’t a speed.