Speed of Surface Waves on Deep Water: G, D, λ

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SUMMARY

The speed of surface waves on deep water is determined by the equation V = √(gλ), where g represents gravitational acceleration and λ denotes the wavelength of the wave. This relationship is derived through dimensional analysis, confirming that the speed V is proportional to the square root of the product of gravitational acceleration and wavelength. The units involved are consistent, with g measured in m/s² and λ in meters, leading to the correct dimensional formulation for wave speed.

PREREQUISITES
  • Understanding of gravitational acceleration (g) in physics
  • Knowledge of wave properties, specifically wavelength (λ)
  • Familiarity with dimensional analysis techniques
  • Basic algebra for manipulating equations and units
NEXT STEPS
  • Study dimensional analysis in physics to strengthen understanding of unit relationships
  • Explore wave mechanics, focusing on the properties of surface waves
  • Learn about gravitational effects on wave speed in different mediums
  • Investigate the implications of the wave speed equation in real-world applications
USEFUL FOR

Students in physics, particularly those studying wave mechanics, as well as educators looking to explain the relationship between gravitational forces and wave behavior in fluids.

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Homework Statement


the speed of surface waves on deep water might depend on the gravitational acceleration has a constant magnitude g,density of water d,and the wavelength of the wave λ.Which one of the following could be how this speed depends on these parameters?(hint:use the dimesional analysis)

there are options for V speed.
the answer is V=√gλ


Homework Equations





The Attempt at a Solution



This was my exam question and i couldn't solve it.Still i have no idea how to solve it. :)
 
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If the units of g is m/s2 and λ is m. Then what is the units of gλ? (Hint: The unit of force x distance = N x m = Nm, use a similar idea to get the combined unit).

After you get the unit, just raise it to the power of 1/2. Treat the m and s like an indicies type problem.
 
thanks :)
 

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