When a source of sound moves past an observer (or rather a listener), the component of the velocity of the source along the line connecting it to the observer determines the change in pitch. If the observer is located directly on the path of the source, the pitch of the sound will change abruptly at the moment when the source is moving “through” the observer. To make this experiment more realistic and safer for the observer, let us analyze what happens when the observer is located off the path of the moving source.
Imagine a racing car traveling at v=210 miles/hour by a spectator located a safe distance d=10 m away from a straight section of the race track. Find how the frequency of the engine (running at 7000 revolutions per minute) heard by the spectator depends on the position of the car along the race track. Make a graph showing this dependence. Indicate the maximum and minimum frequencies and where the pitch starts to change (slide) on the graph. Find the range of positions of the race car over which the pitch changes by 90% of its total variation.