PBL: Doppler effect

Not very angry birds

I've never played angry birds but know it's something to do with throwing birds, I guess that's what makes them angry. We are not going to throw the birds but we'll release them one at a time from a moving truck, this will make them a bit cross but not exactly angry.

The birds in question can fly at 5 ms-1 in still air. They are released one at a time from a truck travelling due North along  a straight road at 2ms-1 . Half of the birds are released from the front the others from the back. The birds travel along the road, the ones at the front forwards and the ones at the back backwards (they travel backwards but fly forwards)

This was supposed to be a joke. The bird is flying with its beak pointing forwards but is released fom the back of the van.

Two twitchers (bird watchers) are waiting by the road about 1km ahead of and 1km behind the truck.

  • If the birds are released one per second how often will they pass each observer?
  • What would happen if the truck increased it's speed?
  • What if the truck went at 5ms-1?
  • How about 6 ms-1?

The birds are released f times per second, the bird speed is c and the speed of the truck is v.

  • Write an expression for the frequency ahead and behind the truck.

The truck now stops but keeps releasing the birds. Calculate the rate at which the birds pass the two observers if they each start to walk towards North at 1 ms-1.

  • If the walkers speed is v write expressions for the rate at which the birds pass.

Explain why this car horn sounds like it does

Try to build a simulation of the moving truck example in Geogebra.

On another day the experiment with the birds is ruined by an old lady feeding the birds at a point 1 km along a line perpendicular to the road. Instead of flying forwards all the birds fly to the food.

  • How will the arrival time of the birds be affected?
  • Try building this one in GeoGebra or Excel.
  • Plot a graph of the difference in frequency vs distance travelled along the road

The truck stops and the old lady goes home because the wind has started to blow at 3 ms-1

  • How does the wind affect the arrival times ahead and behind the truck?
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