Wave Group Velocity
Calculate the group velocity of an ocean wave in deep water, c_g = g·T ÷ (4π), from the period T (s). The result, in m/s, is the speed at which the wave energy (and the 'envelope' of a wave group) propagates — exactly half the celerity (phase velocity) in deep water. This difference explains a curious phenomenon: within a wave group, individual crests appear at the rear, advance through the group (faster than it) and disappear at the front. The group velocity is what matters for energy transport and predicting swell arrival at the coast. Enter the wave period.
Resultado
—
Velocidade de grupo da onda
Existe uma sutileza profunda na física das ondas: as cristas individuais e a energia da onda viajam a velocidades diferentes. A velocidade das cristas é a celeridade (velocidade de fase); a velocidade com que a energia — e a 'envoltória' de um grupo de ondas — se propaga é a velocidade de grupo, que em águas profundas é c_g = g·T ÷ (4π), exatamente a metade da celeridade. Essa diferença produz um fenômeno que se pode observar jogando uma pedra num lago calmo: o grupo de ondulações que se espalha avança como um todo a uma velocidade, mas, olhando de perto, cristas individuais surgem na retaguarda do grupo, avançam através dele (mais rápidas que o grupo), atingem amplitude máxima no centro e desaparecem na dianteira — como se as ondas 'corressem por dentro' do pacote. A velocidade de grupo é a que realmente importa para a engenharia e a oceanografia, porque é ela que transporta a energia. Quando se prevê a chegada de um swell a uma costa distante, é a velocidade de grupo (não a de fase) que determina quando a energia chega. É também a velocidade de grupo que aparece no cálculo do fluxo de potência das ondas (potência = energia × velocidade de grupo). E o conceito vai muito além das ondas do mar: a velocidade de grupo aparece na óptica (a velocidade com que a informação/energia de um pulso de luz viaja num meio dispersivo), na mecânica quântica (a velocidade da partícula associada a um pacote de ondas) e em qualquer fenômeno ondulatório dispersivo. Informe o período da onda.
Related Tools
Deep Water Wave Celerity
Calculate the celerity (phase velocity) of an ocean wave in deep water, c = g·T ÷ (2π), from the period T (s) and gravity g. The result, in m/s, is the speed at which the wave crest propagates. In deep water, longer-period waves travel faster — a phenomenon called dispersion, which makes long-period swell reach the coast before the short waves generated by the same storm. The celerity is half the group velocity (at which energy travels) in deep water. It is a base concept of wave hydrodynamics. Enter the wave period.
Ocean Wavelength
Calculate the wavelength of an ocean wave in deep water, L = g·T² ÷ (2π), from the wave period T (s) and gravity g (9.81 m/s²). The result, in meters, is the distance between two successive crests — in deep water, it depends only on the period. Long-period waves (swell from distant storms) have much larger wavelengths than local wind waves. The wavelength sets the depth at which the wave 'feels' the bottom (about L/2), starts to refract and shoal until it breaks. It is a fundamental parameter of linear wave theory and coastal engineering. Enter the wave period.
Wave Period
Calculate the period of a wave, T = 1 ÷ f, from the frequency f (Hz). The result, in seconds, is the time between two successive crests passing a fixed point — one of the most important properties of an ocean wave. The period determines the wavelength and celerity (in deep water), the depth at which the wave interacts with the bottom, and classifies the sea state: local wind waves have short periods (3-8 s), while swell from distant storms has long periods (10-20 s), travels faster and penetrates deeper. The period is measured by buoys and used in wave forecasting. Enter the wave frequency.
Shallow Water Wave Celerity
Calculate the celerity of a wave in shallow water, c = √(g·h), from the water depth h (m) and gravity g. The result, in m/s, is the propagation speed when the depth is much smaller than the wavelength — a situation in which the wave 'feels' the bottom and its speed depends only on depth, no longer on the period. This is why waves refract as they approach the coast (the deeper part travels faster) and why tsunamis travel at hundreds of km/h in the deep ocean and slow down (piling up energy) as they reach the coast. Enter the water depth.
Wave Power
Estimate the power flux of an ocean wave per meter of wave front, P ≈ 0.5 × H² × T, from the wave height H (m) and the period T (s), in deep water (seawater). The result, in kW/m, is the power available per meter of wave front width — a key indicator of wave energy potential for converters (WECs). Coasts exposed to ocean swells (European Atlantic, Pacific) reach 30-70 kW/m, a significant renewable resource. The power grows with the square of the height and linearly with the period. Enter the wave height and period.
Wave Energy
Calculate the energy density of an ocean wave, E = (1 ÷ 8)·ρ·g·H², from the water density ρ (kg/m³, ~1025 for seawater), gravity g and the wave height H (m). The result, in J/m² (energy per surface area), is the sum of the wave's kinetic and potential energy — proportional to the square of the height, so large waves carry far more energy. It is the basis for calculating wave energy generation potential and the impact on coastal structures and beach erosion. Enter the water density and the wave height.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.