Have you ever listened for an approaching train by kneeling next to a railroad track and putting your ear to the rail? Young's modulus for steel is Y = 2.0 1011 N/m2, and the density of steel is rho = 7860 kg/m3. On a day when the temperature is 19° C, how many times greater is the speed of sound in the rail than in the air? (Treat air as an ideal gas of particles with mass 4.78 10-26 kg and with γ = 1.40.)

Global warming will produce rising sea levels partly due to melting ice caps but also due to the expansion of water as average ocean temperatures rise. to get some idea of the size of this effect, calculate the change in length of a column of water 1.00 km high for a temperature increase of 1.00ºc. note that this calculation is only approximate because ocean warming is not uniform with depth. (answer in ×10^{-3} −3 m)