
Wave Analysis of Traffic Flow
Although a series of cars on the highway appears to be a bunch of
particles, wave analysis can be used to understand traffic
congestion.
Here we will show how the formula for waves is the same as the formula for traffic. We will examine the implications. 
Written 1999
Formatted 2010 

The basic formula is: v = 2df
For a wave: 
For Traffic Flow: 
v represents the velocity of the
wave
d represents to distance between peaks
and troughs ( 1/2 wavelength)
f represents the frequency of the waves
per unit time (typ: second) 
v represents the average car
velocity
d represents the average distance between
drivers
f represents the average number of cars
that pass a point per unit time (typ: minute) 
Now, the basic wave equation applies to traffic.
So, if the average velocity drops, say, due to construction, for the
cars to pass at the same frequency the distance d between the cars must decrease. Is
anything learned yet?
When will highway congestion occur? If we let b represent the typical bumper to bumper length of each car,
we can determine when congestion will occur. When a drop in velocity
forces d<b congestion will occur. 
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