Answers

2015-12-05T12:34:58+05:30
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

dk.


→ 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 :)
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