Consider the surface density wave 01 = 010e (w+30-ar³/4) 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. 01 1. Using mathematical arguments show whether the pattern described by σ₁ is rotating clockwise or anticlockwise. 2. Using mathematical arguments show whether the pattern described by σ is a trailing or a leading spiral.

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Chapter16: Waves
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Consider the surface density wave
01 = 010e (w+30-ar³/4)
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.
01
1. Using mathematical arguments show whether the pattern described by σ₁ is rotating
clockwise or anticlockwise.
2. Using mathematical arguments show whether the pattern described by σ is a trailing
or a leading spiral.
Transcribed Image Text:Consider the surface density wave 01 = 010e (w+30-ar³/4) 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. 01 1. Using mathematical arguments show whether the pattern described by σ₁ is rotating clockwise or anticlockwise. 2. Using mathematical arguments show whether the pattern described by σ is a trailing or a leading spiral.
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