1. Repeat Prob. 4.46 for the case in which the air inside the pipe is flowing from left to right in the direction of the positive x-axis with a flow velocity of: (a) 30m/sec, and {b) 400 m/sec. 2. Consider an element of air in the standard atmosphere at a standard altitude of 1000 m. Assume that you somehow raise this element of air to a standard altitude of 2000 m, where the element now takes on the standard pressure at 2000 m. Calculate the density of this isentropically raised element of air and compare it with the density of its neighboring elements of air that all have a density equal to the standard density at 2000 m. What does this say about the stability of the atmosphere in this case? Prob. 4.46 Consider a long pipe filled with air at standard sea-level conditions. Let x be the longitudinal coordinate measured along the pipe. The air is stationary inside the pipe, i.e., the flow velocity is zero everywhere inside the pipe. A small firecracker is mounted inside the tube at an axial location x = 0. When the firecracker is detonated, two weak pressure disturbances (pressure waves) are created at x = 0 that propagate along the pipe, one to the right and the other to the left. Assume that these weak pressure distributions travel at the local speed of sound. Using SI units, calculate: {a) the speed of the waves relative to the pipe, and {b) the x-location of each wave 0.2 seconds after detonation of the firecrackers.

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