An ambulance is traveling East at 20m/s. The siren emits a fixed frequency of 22

Question

An ambulance is traveling East at 20m/s. The siren emits a fixed frequency of 220Hz. Each of the following cars is traveling down the road as described. Rank the cars according to the frequency the driver will hear. Select 1 for the car which will hear the highest frequency. Remember that if the frequency is the same, select the same rank and skip the next number. I really suggest drawing a picture to help sort this out. Keep in mind the relative speed - How fast does it seem the ambulance is moving towards or away from each driver?

1

2

3

4
  A car driving West at a speed of 25m/s. The car has already passed the ambulance.

1

2

3

4
  A car driving East at a speed of 20m/s. The car is behind the ambulance.

1

2

3

4
  A car driving West at a speed of 15m/s. The car is moving towards the ambulance.

1

2

3

4
  A car sitting stationary at the side of the road watching the oncoming ambulance.

Explanation / Answer

Speed and frequency of source (ambulance)

vs = 20m/s,    fs= 220Hz

Case (A) : A car driving West at a speed of vo=25m/s. The car has already passed the ambulance.

In this case, the observer (car driver) is moving away from the the source. So, using below formula

fA'=[(v+vo)/(v+vs)] fs

Also, since both vehicles are moving at right angles to each other we will use vs cos(90) instead of vs.vs cos(90) will give zero, so elliminate the vs term from above formula

fA' = [(v+vo)/(v)] fs = [(343+25)/343] (220)

fA' = 236.03 Hz

Case (B) : A car driving East at a speed of vo=20m/s. The car is behind the ambulance.

Inn this case, the obeserver is approaching the source. Also, both are moving in the same direction. So, using below formula

fB' = [(v+vo)/(v-vs)] fs = [(343+20)/(343-20)] (220)

fB' = 247.24 Hz

Case (C) : A car driving West at a speed of vo=15m/s. The car is moving towards the ambulance.

In this case, the observer is moving towards the source. So, using below formula

fC'=[(v+vo)/(v-vs)] fs

Also, since both vehicles are moving at right angles to each other we will use vs cos(90) instead of vs.vs cos(90) will give zero, so elliminate the vs term from above formula

fC' = [(v+vo)/(v)] fs = [(343+15)/343] (220)

fC' = 229.62 Hz

Case (D) : A car sitting stationary at the side of the road watching the oncoming ambulance. vo=0m/s

In this case, the source is approaching the stationary observer. So, using below formula

fD' = [(v+vo)/(v-vs)] fs = [(343+0)/(343-20)] (220)

fD' = 233.62 Hz

Ranking all the four cases

fA' = 236.03 Hz   ------------------ (2)

fB' = 247.24 Hz   ------------------- (1)

fC' = 229.62 Hz --------------- (4)

fD' = 233.62 Hz ----------------- (3)

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