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 star's radius varies periodically with time, with a displacement anti node at the star's surface.

(a) Would you expect the center of the star to be a displacement node or anti node?

(b) By analogy with a pipe with one open end, show that the period of pulsation Z is given by T = 4R/v, where R is the equilibrium radius of the star and v is the average sound speed in the material of the star.

(c) Typical white dwarf stars ate composed of material with a bulk modulus of 1.33 x 1022 Pa and a density of 1010 kg/m3. They have radii equal to 9.0 x 10-3 solar radius. What is the approximate pulsation period of a white dwarf?