A.at pattern. Let'sssuming that thee angular spatialporal frequenciesw, correspond toe is thenW, 1)ir)[7.33]avelength of thequals the groupeing amplitude-e waves of fre-of modulatingand sum overis called thewer sideband.7.19 Given the dispersion relation w = ak', compute both the phaseand group velocities.-7.20* Using the relation 1/v = dk/dv. prove that1VgIV₂7.21* In the case of lightwaves, show thatV =1Vev dvv² dvV7.22 The speed of propagation of a surface wave in a liquid of depthmuch greater than λ is given byv dnc dv11-+-Csolve 7.25 onlywhere g = acceleration of gravity, λ = wavelength, p = density. Y= surface tension. Compute the group velocity of a pulse in the longwavelength limit (these are called gravity waves).7.23* Show that the group velocity can be written asdvdλ7.24 Show that the group velocity can be written asgλ2πΥ+2πT pλVg = V-A(n + w(dn/dw)7.25 With the previous problem in mind prove thatdn (v)dvn₂ = n(v) + v.i need clear ans by handand solve very very fastin 20 min and thank youDYBALA

For the expression from problem 7.24 vg = cn+ ωdndω

Answered: 7.25 With the previous problem in mind…

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7.25 With the previous problem in mind prove that dn (v) dv n₂ = n(v) + v i need clear ans

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Chapter1: Units, Trigonometry. And Vectors

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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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A.
at pattern. Let's
ssuming that the
e angular spatial
poral frequencies
w, correspond to
e is then
W, 1)
ir)
[7.33]
avelength of the
quals the group
eing amplitude-
e waves of fre-
of modulating
and sum over
is called the
wer sideband.
7.19 Given the dispersion relation w = ak', compute both the phase
and group velocities.
-7.20* Using the relation 1/v = dk/dv. prove that
1
Vg
I
V₂
7.21* In the case of lightwaves, show that
V =
1
Ve
v dv
v² dv
V
7.22 The speed of propagation of a surface wave in a liquid of depth
much greater than λ is given by
v dn
c dv
11
-+-
C
solve 7.25 only
where g = acceleration of gravity, λ = wavelength, p = density. Y
= surface tension. Compute the group velocity of a pulse in the long
wavelength limit (these are called gravity waves).
7.23* Show that the group velocity can be written as
dv
dλ
7.24 Show that the group velocity can be written as
gλ
2πΥ
+
2πT pλ
Vg = V-A
(
n + w(dn/dw)
7.25 With the previous problem in mind prove that
dn (v)
dv
n₂ = n(v) + v.
i need clear ans by hand
and solve very very fast
in 20 min and thank you
DYBALA

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