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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Relativistic Energy and Momentum

According to classical physics, time flow is the same for every observer. But according to einstein's theory, time flow is different for different observers. The idea that time flow is not the same for all may sound strange because we may not experience this effect in everyday life. This effect is only observed when an object moves with some velocity comparable to the velocity of light. This velocity is termed relativistic velocity.

Question

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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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