Fig. 2 - Curves showing variation of pressure with time at 
two fixed points 
For times satisfying equation 4 the respective ordinates are a constant 
time apart and, therefore 
P'Q' = ri/T2 PQ ece eee eoe eco eee eee coe (6) 
It follows that the curve A'B'C' can be obtained from the curve ABC by 
displacing curve ABC a distance (r, - r2)/e to the right and reducing all 
the pressure ordinates in the same ratio r,/% e The two curves can, 
therefore, be made of the same shape by changing only the pressure scale. 
14. Expressed physically, the pressure/time variation et any distance n is 
repeated on a reduced pressure scale r,/r, at greater distance r, at a time 
(r, - r,)/e later. Subject to the reduction in magnitude, the pressure in 
the pulse thus travels a distance (r, - r,) in time (r, - r,)/e which 
corresponds to a constant velocity of propagation, c independent of r, or 
r,- Equation 1 thus represents a wave travelling outwards with constant 
velocity ¢ and giving pressure/time variations at different points similar 
to those illustrated in fig. 2. 
Variation of pressure with distance (time constant) 
15- Now consider the variation of the pressure in the pulse with distance. 
This variation is illustrated in fig. 3 for two given times t, and t, by 
the curves DEF and D'E'F' respectively. 
