b) Consider the surface density wave 01 = σι 010e² (wt+40+ar³) " [4 marks] where t is time, the azimuthal angle, which increases clockwise, and r the radial coordi- nate. w is the angular frequency (w > 0), a is a positive constant. 10 is the amplitude of the wave. 1. Using mathematical arguments show whether the pattern described by σ ₁ is rotating clockwise or anticlockwise. [5 marks] 2. Using mathematical arguments show whether the pattern described by σ is a trailing or a leading spiral. [5 marks] 3. Consider now a point Po at a distance r = 5kpc from the centre C of the spiral. The point Po is at a peak of the surface density wave. Going outward from Po along the line passing through C and Po, and using a = (3kpc) determine the distance between C and the next peak of the surface density wave. -3 [5 marks]
b) Consider the surface density wave 01 = σι 010e² (wt+40+ar³) " [4 marks] where t is time, the azimuthal angle, which increases clockwise, and r the radial coordi- nate. w is the angular frequency (w > 0), a is a positive constant. 10 is the amplitude of the wave. 1. Using mathematical arguments show whether the pattern described by σ ₁ is rotating clockwise or anticlockwise. [5 marks] 2. Using mathematical arguments show whether the pattern described by σ is a trailing or a leading spiral. [5 marks] 3. Consider now a point Po at a distance r = 5kpc from the centre C of the spiral. The point Po is at a peak of the surface density wave. Going outward from Po along the line passing through C and Po, and using a = (3kpc) determine the distance between C and the next peak of the surface density wave. -3 [5 marks]
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
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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Question
![b) Consider the surface density wave
01 =
σι 010e² (wt+40+ar³)
"
[4 marks]
where t is time, the azimuthal angle, which increases clockwise, and r the radial coordi-
nate. w is the angular frequency (w > 0), a is a positive constant. 10 is the amplitude of
the wave.
1. Using mathematical arguments show whether the pattern described by σ ₁ is rotating
clockwise or anticlockwise.
[5 marks]
2. Using mathematical arguments show whether the pattern described by σ is a trailing
or a leading spiral.
[5 marks]
3. Consider now a point Po at a distance r = 5kpc from the centre C of the spiral. The
point Po is at a peak of the surface density wave. Going outward from Po along the line
passing through C and Po, and using a = (3kpc) determine the distance between C
and the next peak of the surface density wave.
-3
[5 marks]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6666f43e-1f68-42b0-bd30-30221842bb87%2Fa14adbf2-cd8c-415b-a9cc-aa10a9d22c01%2Fsoywrcf_processed.png&w=3840&q=75)
Transcribed Image Text:b) Consider the surface density wave
01 =
σι 010e² (wt+40+ar³)
"
[4 marks]
where t is time, the azimuthal angle, which increases clockwise, and r the radial coordi-
nate. w is the angular frequency (w > 0), a is a positive constant. 10 is the amplitude of
the wave.
1. Using mathematical arguments show whether the pattern described by σ ₁ is rotating
clockwise or anticlockwise.
[5 marks]
2. Using mathematical arguments show whether the pattern described by σ is a trailing
or a leading spiral.
[5 marks]
3. Consider now a point Po at a distance r = 5kpc from the centre C of the spiral. The
point Po is at a peak of the surface density wave. Going outward from Po along the line
passing through C and Po, and using a = (3kpc) determine the distance between C
and the next peak of the surface density wave.
-3
[5 marks]
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