Two ambulances sounding identical sirens of rest frequency f0 travel along the same straight road in the same direction. Ambulance A follows 50 m behind Ambulance B. Both vehicles initially travel at the same speed so that a roadside observer hears a single steady pitch. At time t=0, Ambulance A suddenly accelerates and quickly reaches a greater constant speed, while Ambulance B maintains its original speed.
As the two Doppler-shifted sounds from the ambulances reach the observer, the superposition produces audible beats whose rate rises, reaches a maximum, and then falls as time progresses.
(a) Describe the physical condition that must be satisfied for an observer to perceive beats between two sound waves.
(b) Explain qualitatively why the beat frequency heard by the roadside observer begins at zero, increases to a maximum, and then decreases again after Ambulance A has passed Ambulance B.
(c) Identify the approximate instant (before, during, or after the overtaking event) at which the observer hears the greatest beat frequency, and justify your answer using the relative motions of the two ambulances and the observer.
(d) If the observer instead rode in a car moving in the same direction as the ambulances at a speed equal to Ambulance B’s original speed, describe how the time variation of the beat frequency would differ from that in parts (a)–(c). Provide a brief explanation based on relative velocities.