2016 USA Physics Olympiad Exam Part A Part A Question Al The Doppler effect for a source moving relative to a stationary observer is described by fo f=1-(v/c)cos0 where f is the frequency measured by the observer,fo is the frequency emitted by the source,v is the speed of the source,c is the wave speed,and 6 is the angle between the source velocity and the line between the source and observer.(Thus 6=0 when the source is moving directly towards the observer and 6=when moving directly away.) A sound source of constant frequency travels at a constant velocity past an observer,and the observed frequency is plotted as a function of time: 450 448 00 00 oObserved Frequency 0 446 444 442 440 到 438 436 434 0 432 0 430 428 0 426 424 0 0 0 422 0000 42 0 2 345 67 891011121314 Time (s) The experiment happens in room temperature air,so the speed of sound is 340 m/s. a.What is the speed of the source? b.What is the smallest distance between the source and the observer? Copyright C2016 American Association of Physics Teachers2016 USA Physics Olympiad Exam Part A 3 Part A Question A1 The Doppler effect for a source moving relative to a stationary observer is described by f = f0 1 − (v/c) cos θ where f is the frequency measured by the observer, f0 is the frequency emitted by the source, v is the speed of the source, c is the wave speed, and θ is the angle between the source velocity and the line between the source and observer. (Thus θ = 0 when the source is moving directly towards the observer and θ = π when moving directly away.) A sound source of constant frequency travels at a constant velocity past an observer, and the observed frequency is plotted as a function of time: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 420 422 424 426 428 430 432 434 436 438 440 442 444 446 448 450 Time (s) Frequency (Hz) Observed Frequency The experiment happens in room temperature air, so the speed of sound is 340 m/s. a. What is the speed of the source? b. What is the smallest distance between the source and the observer? Copyright c 2016 American Association of Physics Teachers