The phase velocity of the waves on a liquid surface is given by Vp = (4π2A/λ2ρ)1/2....
The phase velocity of the waves on a liquid surface is given by Vp = (4π2A/λ2ρ)1/2. A shows the surface tension A, and ρ shows the density of the liquid. Find the group velocity (in phase velocity) of the waves.
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The phase velocity of the waves on a liquid surface is given by
Vp =
(4π2A/λ2ρ)1/2....
Waves of length 12 m propagate in water of depth 3 m. Determine the phase velocity...
Waves of length 12 m propagate in water of depth 3 m. Determine the phase velocity AND group velocity of these waves. Ignore all interactions with the air. Phase speed is [c] m/s Use g = 9.8 m/s^2 and ρ = 1000 kg/m^3. Write the answer to the nearest tenth in units of: m/s.
7. (i) The dispersion relation for surface water waves on deep water is given by w?...
7. (i) The dispersion relation for surface water waves on deep water is given by w? = gk. Show that the group velocity is Vg = g/(2w). Derive an expression relating the phase velocity Vp and the group velocity vg and hence determine if the dispersion is normal or anomalous. What are the physical significances of Vg and vp? [7 marks] Now consider a propagating wavepacket with initial length Lo. (ii) Use the bandwidth theorem to show that the minimum...
1.Vp and Vg are the phase velocity and group velocity, respectively, of the de Broglie wave...
1.Vp and Vg are the phase velocity and group velocity, respectively, of the de Broglie wave for an electron moving with the velocity V, and C is the velocity of light in free space. Which of the following is incorrect? (a) Vp> Vg (b) Vp>C (c) Vg<C (d) Vg=V (e) Vp=V 2.An atomic force microscope (AFM) probe is essentially a cantilever with a nanosized tip at the free end. One scan mode of AFM is to drive the probe as...
(30 marks) For water waves with wavelength much longer than Xo, the effect of surface tension...
(30 marks) For water waves with wavelength much longer than Xo, the effect of surface tension can be neglected. These waves are called gravity waves. =%and find its value given σ=0.073 N/m and ρ: 10000 kg/ms fr (a) Show that water at 20°C. (b) Gravity waves with kh » are called deep gravity waves. Deep gravity waves generated by a storm arrived at the coast have a period of about 15 seconds. A day later, the period of the waves...
a viscous and surface-tension effects are neglected, the velocity V of eflux of liquid from a...
a viscous and surface-tension effects are neglected, the velocity V of eflux of liquid from a reservoiris thought to depend upon the pressure drop Ap of the liquid and its density p. Determine the form of expression for V
Use a computer algebra system to find the rate of mass flow of a fluid of density ρ through the surface S oriented upward if the velocity field is given by F(x, y, z) 0.52k Use a computer algebr...
Use a computer algebra system to find the rate of mass flow of a fluid of density ρ through the surface S oriented upward if the velocity field is given by F(x, y, z) 0.52k
Use a computer algebra system to find the rate of mass flow of a fluid of density ρ through the surface S oriented upward if the velocity field is given by F(x, y, z) 0.52k
1- a) On this phase diagram, indicate 1) a melting point 2) a boiling...
1- a) On this phase diagram,
indicate
1) a melting
point
2) a boiling
point
3) a sublimation
point
4) the critical
point
5) a triple
point
6) an isotheral
change
7) an isobaric
change
8) a point where
the degrees of freedom = 2
b) A liquid
rises 5.85 cm in a capillary of diameter 0.300 mm. The density of
the liquid is 0.81 g/cm3. The
density of air...
24 pts. Phase and group velocity of a plasma. The permittivity ε of a plasma (ionized gas) is a f...
24 pts. Phase and group velocity of a plasma. The permittivity ε of a plasma (ionized gas) is a function of frequency given by: I. Eo where co is radian frequency and o the "plasma frequency", which is assumed to be a constant related to the properties of the ionized gas. (a) 6 pts. Given the relation above, write an expression for the phase velocity in a plasma. (Assume μ-,-1). (b) 2 pts. Write an expression for the magnitude of...
24 pts. Phase and group velocity of a plasma. The permittivity ε of a plasma (ionized...
24 pts. Phase and group velocity of a plasma. The permittivity ε of a plasma (ionized gas) is a function of frequency given by: I. Eo where co is radian frequency and o the "plasma frequency", which is assumed to be a constant related to the properties of the ionized gas. (a) 6 pts. Given the relation above, write an expression for the phase velocity in a plasma. (Assume μ-,-1). (b) 2 pts. Write an expression for the magnitude of...
1. Rate of vaporization of a liquid II. Surface tension of a liquid III. Molarity of...
1. Rate of vaporization of a liquid II. Surface tension of a liquid III. Molarity of an aqueous salt solution Which of the given above decrease(s) when temperature is raised? Your answer: Only! Only 11 Only is 1 and 11 Olland III
7. (i) The dispersion relation for surface water waves on deep water is given by w? = gk. Show that the group velocity is Vg = g/(2w). Derive an expression relating the phase velocity Vp and the group velocity vg and hence determine if the dispersion is normal or anomalous. What are the physical significances of Vg and vp? [7 marks] Now consider a propagating wavepacket with initial length Lo. (ii) Use the bandwidth theorem to show that the minimum...
(30 marks) For water waves with wavelength much longer than Xo, the effect of surface tension can be neglected. These waves are called gravity waves. =%and find its value given σ=0.073 N/m and ρ: 10000 kg/ms fr (a) Show that water at 20°C. (b) Gravity waves with kh » are called deep gravity waves. Deep gravity waves generated by a storm arrived at the coast have a period of about 15 seconds. A day later, the period of the waves...
a viscous and surface-tension effects are neglected, the velocity V of eflux of liquid from a reservoiris thought to depend upon the pressure drop Ap of the liquid and its density p. Determine the form of expression for V
Use a computer algebra system to find the rate of mass flow of a fluid of density ρ through the surface S oriented upward if the velocity field is given by F(x, y, z) 0.52k
Use a computer algebra system to find the rate of mass flow of a fluid of density ρ through the surface S oriented upward if the velocity field is given by F(x, y, z) 0.52k
1- a) On this phase diagram,
indicate
1) a melting
point
2) a boiling
point
3) a sublimation
point
4) the critical
point
5) a triple
point
6) an isotheral
change
7) an isobaric
change
8) a point where
the degrees of freedom = 2
b) A liquid
rises 5.85 cm in a capillary of diameter 0.300 mm. The density of
the liquid is 0.81 g/cm3. The
density of air...
24 pts. Phase and group velocity of a plasma. The permittivity ε of a plasma (ionized gas) is a function of frequency given by: I. Eo where co is radian frequency and o the "plasma frequency", which is assumed to be a constant related to the properties of the ionized gas. (a) 6 pts. Given the relation above, write an expression for the phase velocity in a plasma. (Assume μ-,-1). (b) 2 pts. Write an expression for the magnitude of...
24 pts. Phase and group velocity of a plasma. The permittivity ε of a plasma (ionized gas) is a function of frequency given by: I. Eo where co is radian frequency and o the "plasma frequency", which is assumed to be a constant related to the properties of the ionized gas. (a) 6 pts. Given the relation above, write an expression for the phase velocity in a plasma. (Assume μ-,-1). (b) 2 pts. Write an expression for the magnitude of...
1. Rate of vaporization of a liquid II. Surface tension of a liquid III. Molarity of an aqueous salt solution Which of the given above decrease(s) when temperature is raised? Your answer: Only! Only 11 Only is 1 and 11 Olland III
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