TABLE 1
In this table y denotes the ratio of the pressures on the two sides of the shock front, U the shock velocity, u the mass velocity behind the front (both in a frame of reference in which the mass velocity in the undisturbed region is zero), c the velocity of sound immediately behind the shock front, P = 5c+u and Q = 5c-u.
| y | U/a | u/a | c/a | y1/7 | P/a | Q/a |
| 1.0 | 1.000 | 0.000 | 1.000 | 1.000 | 5.000 | 5.000 |
| 1.1 | 1.042 | 0.069 | 1.014 | 1.014 | 5.137 | 5.000 |
| 1.2 | 1.082 | 0.132 | 1.026 | 1.026 | 5.265 | 5.001 |
| 1.3 | 1.121 | 0.191 | 1.038 | 1.038 | 5.384 | 5.001 |
| 1.4 | 1.159 | 0.247 | 1.050 | 1.049 | 5.496 | 5.002 |
| 1.5 | 1.195 | 0.299 | 1.061 | 1.059 | 5.602 | 5.005 |
| 1.6 | 1.231 | 0.348 | 1.071 | 1.069 | 5.704 | 5.007 |
| 1.7 | 1.265 | 0.395 | 1.081 | 1.078 | 5.801 | 5.010 |
| 1.8 | 1.298 | 0.440 | 1.091 | 1.087 | 5.894 | 5.014 |
| 1.9 | 1.331 | 0.483 | 1.100 | 1.095 | 5.984 | 5.018 |
| 2.0 | 1.363 | 0.524 | 1.109 | 1.104 | 6.071 | 5.023 |
| 2.1 | 1.394 | 0.564 | 1.118 | 1.112 | 6.155 | 5.027 |
| 2.2 | 1.424 | 0.602 | 1.127 | 1.119 | 6.237 | 5.034 |
| 2.3 | 1.454 | 0.639 | 1.136 | 1.127 | 6.318 | 5.040 |
| 2.4 | 1.483 | 0.674 | 1.144 | 1.133 | 6.395 | 5.047 |
| 2.5 | 1.512 | 0.709 | 1.152 | 1.140 | 6.470 | 5.053 |
It would accordingly appear that a significant case of shock pulses is provided by neglecting entropy changes and considering Q as a constant throughout. As we shall see this leads to an interesting class of shock solutions which does not appear to have been isolated so far.
2. The Solutions for a Special Class of Shock Pulses for which Q = Constant. Measuring the velocities in units of the velocity of sound in the undisturbed air in front of the shock, the equations of motion in Riemann's form are (cf. Penney, R. C., 260; also, the Appendix to this paper)
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