A state trooper chases a speeder along a straight road; with vehicles move at 160 km/h. the siren on the trooperâs vehicle produces sound at a frequency of 500 hz. what is the doppler shift inthe frequency heard by the speeder

Since both the speeder and the state trooper are moving at the same speed and same direction, therefore there would be no or zero Doppler shift.

In order to have a Doppler shift, the distance or separation between the state trooper and the speeder must also be changing with time. Which in this case, the distance remains the same or constant since they are moving alike. This is just like what would occur if they were both standing still or parked.

So this further means that the frequency of sound is the same as the frequency heard by the speeder. Therefore the Doppler "shift" of the frequency on the speeder would be zero.