A. A flat bottomed bowl of radius R is filled with water to depth H. (a) Estimate the period, P, of the sloshing mode. (b) Estimate the damping timescale, T, in the small amplitude limit. (c) Evaluate P and T for the Earth's ocean basin.
B. Derive an expression for the luminosity of a pulsar with a dipole field. The field strength is B at the surface of the star, the stellar radius is R, and its spin frequency is Omega. Repeat for a pulsar with a quadrupole field.
C. The CO molecule has a permanent electric dipole moment, while molecular hydrogen H2 has only a permanent quadrupole moment. Set both molecules rotating at the same frequency. Estimate the factor by which the power radiated by the CO molecule exceeds the power radiated by the H2 molecule.
D. Whistling tea kettles. (a) It takes about 5 minutes to boil a liter of water on a kitchen stove. (i) How much power is used to heat the water? (ii) At what rate does the boiling water evaporate? (b) The basic tea kettle whistle is a hole of radius 0.15 cm. (i) At what velocity does water vapor exit the hole when water is boiling inside the kettle? (ii) What is the Reynolds number of the flow near the hole? Would you expect von Karman vortices to be shed? (iii) Estimate the frequency of the kettle whistle. (iv) Estimate the radiated acoustic power.
E. Following a winter storm, the interval between waves at California beaches declined from 17-19 s on Sunday, to 16-18s on Monday, and to 15-16s on Tuesday. Typical values are 10-11 s. (a) What was the maximum sustained wind speed during the storm? (b) How distant was the storm from the beaches? (c) How long ago did the storm take place? (d) What are upper limits on the size and duration of the storm?
F. Derive an analytic expression for the 5 minute oscillation period of the Sun.