Yiyun (Lily) ZhangL2C

Physics 101

Learning Objective

A police officer is standing behind a tree on the sidewalk. He has a speed gun pointed at the oncoming traffic but for a moment he is distracted and forgets to check the speed gun as a grey minivan speeds past him. The frequency which the police officer hears the minivan after it passes him is 459HZ. Assuming a typical minivan engine operates at 500Hz and the speed sound in air is 343m/s, and if the speed limit is 90km/hr was the minivan speeding?

picture from google http://media.winnipegfreepress.com/images/093009_speedtrap_01.jpg

Answer

Relevant formulas

f r=

ѵ± ѵ r¿

ѵ ±ѵ sf s¿

In this question we know:

ѵ= speed of light in air

=343 m/s

f r= frequency which the receiver hears

= 459Hz

f❑s = frequency of the source sound, which is the engine of the minivan

Yiyun (Lily) ZhangL2C

= 500 Hz

Finally, in this question we need to find the velocity of the source (the minivan). But to find that we need the velocity of the receiver. Since the receiver (the police officer) is not moving, his velocity is zero!

ѵ r = velocity of receiver

=0

We now know that we want to find ѵ s, but how do we know that if its + or - ѵ s ? Since the

frequency given is the frequency the police officer hears after the minivan passes him it is + ѵ s.Rearranging the equation to solve for ѵ s

f r (ѵ+ѵ s )=ѵ f s

(ѵ+ѵ s )=ѵ f sf r

ѵ s=ѵ f sf r

−ѵ

ѵ s=

343ms

∗500Hz

459Hz−343ms

ѵ s=¿ 30.6ms

∗3600 s

hr∗1km

1000m

ѵ s=110kmhr

The verdict, yes the minivan was speeding! Lucky break for the driver that the police officer was distracted!