Shock waves that occur in traffic flow are very similar to the waves produced by dropping stones in water. A shock wave propagates along a line of vehicles in response to changing conditions at the front of the line. Shock waves can be generated by collisions, sudden increases in speed caused by entering free flow conditions, or by a number of other means. Basically, a shock wave exists whenever the traffic conditions change.
The equation that is used to estimate the propagation velocity of shock waves is given below.
vsw = (qb qa)/(kb ka)
Note the magnitude and direction of the shock wave.
(+) Shock wave is travelling in same direction as traffic stream.
For example, lets assume that an accident has occurred and that the flow after the accident is reduced to zero. Initially, the flow was several vehicles per hour. Also, the density is much greater after the accident. Substituting these values into the shock wave equation yields a negative (-) propagation velocity. This means that the shock wave is traveling against the traffic. If you could look down on this accident, you would see a wave front, at which vehicles began to slow from their initial speed, passing from vehicle to vehicle back up the traffic stream. The first car would notice the accident first, followed an instant later by the second car. Each vehicle begins slowing after its driver recognizes that the preceding vehicle is slowing.