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

1
by goutamsahoo7

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by goutamsahoo7

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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 :)