The Doppler effect for a source moving relative to a stationary observer is described by
where f is the frequency measured by the observer, f_{0} is the frequency emitted by the source, v is the speed of the source, c is the wave speed, and \theta is the angle between the source velocity and the line between the source and observer. (Thus \theta=0 when the source is moving directly towards the observer and \theta=\pi 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:
The experiment happens in room temperature air, so the speed of sound is 340 \mathrm{~m} / \mathrm{s}.
a. What is the speed of the source?
b. What is the smallest distance between the source and the observer?