The period of a pulsating variable star may be estimated by considering the star to be executing radial longitudinal pulsations in the fundamental standing wave mode; that is, the radius varies periodically with the time, with a displacement antinode at the surface. (a) Would you expect the center of the star to be a displacement node or antinode? (b) By analogy with the open organ pipe, show that the period of 4R pulsation T is given by T = , where R is the equilibrium radius of the star and v, is the average sound speed. (c) Typical white dwarf stars are composed of material with a bulk modulus of 1.33 x 1022 Pa and a density of 1.0 x 1010 kg/m³. They have radii equal to 0.009 solar radius. What is the approximate pulsation period of a white dwarf?
The period of a pulsating variable star may be estimated by considering the star to be executing radial longitudinal pulsations in the fundamental standing wave mode; that is, the radius varies periodically with the time, with a displacement antinode at the surface. (a) Would you expect the center of the star to be a displacement node or antinode? (b) By analogy with the open organ pipe, show that the period of 4R pulsation T is given by T = , where R is the equilibrium radius of the star and v, is the average sound speed. (c) Typical white dwarf stars are composed of material with a bulk modulus of 1.33 x 1022 Pa and a density of 1.0 x 1010 kg/m³. They have radii equal to 0.009 solar radius. What is the approximate pulsation period of a white dwarf?
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Transcribed Image Text:4. The period of a pulsating variable star may be estimated by considering the star to be executing radial
longitudinal pulsations in the fundamental standing wave mode; that is, the radius varies periodically with
the time, with a displacement antinode at the surface. (a) Would you expect the center of the star to be a
displacement node or antinode? (b) By analogy with the open organ pipe, show that the period of
4R
pulsation T is given by T = *, where R is the equilibrium radius of the star and v, is the average
sound speed. (c) Typical white dwarf stars are composed of material with a bulk modulus of 1.33 x
1022 Pa and a density of 1.0 x 1010 kg/m³. They have radii equal to 0.009 solar radius. What is the
approximate pulsation period of a white dwarf?
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