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

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

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A eat pattern. Let's ssuming that the e angular spatial Doral frequencies , correspond to e is then w, 1) [7.33] avelength of the quals the group 51) eing amplitude- e waves of fre- of modulating and sum over is called the wer sideband. 7.19 Given the dispersion relation w = and group velocities. 7.20* Using the relation 1/v = dk/dv. prove that 1 Ve 7.21* In the case of lightwaves, show that 1 V V= 1 11 C Vg v dv 2² = + ak², compute both the phase V = 7.22 The speed of propagation of a surface wave in a liquid of depth much greater than A is given by v dn c dv solve 7.25 only dv where g = acceleration of gravity, A = 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 Vg = V-A gλ 2πΥ + 2πT pλ dv dλ 7.24 Show that the group velocity can be written as C 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 A DYBALA
Transcribed Image Text:A eat pattern. Let's ssuming that the e angular spatial Doral frequencies , correspond to e is then w, 1) [7.33] avelength of the quals the group 51) eing amplitude- e waves of fre- of modulating and sum over is called the wer sideband. 7.19 Given the dispersion relation w = and group velocities. 7.20* Using the relation 1/v = dk/dv. prove that 1 Ve 7.21* In the case of lightwaves, show that 1 V V= 1 11 C Vg v dv 2² = + ak², compute both the phase V = 7.22 The speed of propagation of a surface wave in a liquid of depth much greater than A is given by v dn c dv solve 7.25 only dv where g = acceleration of gravity, A = 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 Vg = V-A gλ 2πΥ + 2πT pλ dv dλ 7.24 Show that the group velocity can be written as C 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 A DYBALA
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