Physics

Problem

For shallow-water gravity waves of wavelength much larger than the depth, laboratory observations suggest that the speed

v

of the wave is given by

v = C\sqrt{gh},

where

g

is the acceleration due to gravity and

h

is the depth of water. (a) Determine the dimensions of the proportionality constant

C

. (b) If

h = 1.0\,\text{m}

and

g = 9.8\,\text{m\,s}^{-2}

, estimate the wave speed when

C

is taken to be unity.