Question

for surface waves in shallow water the frequency and wavelength are connected through the relation

Answer 1

heyy i found the answer!

For surface waves in shallow water, the frequency and wavelength are connected through the relation
f = √
2πS
ρλ
3
where S and ρ respectively denote surface tension and density of water. Calculate the group velocity of 
waves. How is it related to phase velocity?
Solution
vg =
ω = 2πf, k =
dk (√
d
vg =
) =
√
3
3
Sk
2
ρ
dω
dk.
2π
2π
→ λ =
λ
√
Sk
2πS
3
=
2
ρ
k
3
λf.
ρλ =
2
The phase velocity is
vp = λf.
Thus,
vg =
3
vp.
2

hope it helps ! 

thanks sean :)