<p><a name=\"11\"> <p>&#160;Two identical police cars are chasing a robber.&#160

Question

<p><a name="11">
<p>&#160;Two identical police cars are chasing a robber.&#160; When at rest, their sirens have a frequency of 539 Hz.&#160; A stationary observer watches as the two cars approach.&#160; The siren of one car (#1) has a frequency of 584 Hz, while the other (#2) has a frequency of 723 Hz.</p>
</a></p>
<p>A) What are the speeds of Car 1 and Car 2</p>
<p>B)&#160;<a name="18">
<p>If the robber hears a frequency of 658 Hz from car #2, what is the speed of the robber?</p>
</a></p>

Explanation / Answer

n1 = 539 Hz = n2

n1' = 584 Hz

n2' = 723 Hz

V = 340 m/s

Velocity of robber, Vo = 0

Velocity of car 1 = V1

Velocity of car 2 = V2

n1' = n1(V - V0) / (V - V1)

V1 = V - n1(V - V0) /n1'   = 26.2 m/s

So velocity of car 1, V1 = 26.2 m/s

We have,

n2' = n2(V - V0) / (V - V2)

V2 = V - n2(V - V0) /n2'   = 86.5 m/s

So velocity of car 2, V2 = 86.5 m/s

If the robber hears sound of frequency 658 Hz from car 2, then

n2 = 658 Hz

n2' = n2(V - V0) / (V - V2)

V0 = V - [(V - V2)n2' / n2 ] = 0.04 m/s

So the robber velocity, V0 = 0.04 m/s

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