6. The Doppler effect causes a change in the perceived frequency of a moving source of
sound. Suppose an ambulance is moving with constant speed down a road, and a listener
is standing next to the road on a footpath. Why does the frequency of the ambulance siren
appear to change most abruptly when it passes closest to the listener?
a. Because this is where the greatest change of relative velocity occurs
b. Because the Doppler effect acts most strongly at short distances
c. Because human hearing is more sensitive to the frequency of louder sounds
d. All of the above
MCQ Question
The frequency of the ambulance siren changes most abruptly when it passes closest to the listener due to the rapid shift in the component of the source’s velocity along the line connecting the source and observer. This occurs because the relative radial velocity reverses sign instantly at the point of closest approach, causing a sudden drop from higher to lower frequency.
Option Analysis
a. Because this is where the greatest change of relative velocity occurs
Correct. The Doppler shift depends on the radial velocity (component toward/away from the listener). Far away, this component changes gradually; at closest approach, it switches from approaching (positive shift) to receding (negative shift) abruptly, maximizing the frequency change rate.
b. Because the Doppler effect acts most strongly at short distances
Incorrect. The Doppler formula \( f’ = f \frac{v}{v \pm v_s \cos \theta} \) shows the shift magnitude depends on cos θ and speeds, not distance directly. Intensity changes with distance, but frequency shift does not.
c. Because human hearing is more sensitive to the frequency of louder sounds
Incorrect. Loudness peaks at closest approach due to the inverse-square law, but the abrupt frequency change is kinematic (velocity-based), not perception-based. Hearing sensitivity varies, but the shift’s abruptness is objective.
d. All of the above
Incorrect. Only option (a) explains the abruptness correctly.
Physics Behind Abrupt Shift
When the ambulance approaches, sound waves compress, increasing frequency (\(f’ > f\)). At closest approach, the motion is perpendicular to the listener, so cos θ = 0, and the perceived frequency briefly equals the actual source frequency. After passing, waves stretch, lowering the frequency (\(f’ < f\)).
This greatest change of relative velocity happens at the instant of closest approach, where the radial component of velocity reverses direction rapidly — from positive (approaching) to negative (receding).
Real-World Examples
- Sirens sound higher-pitched as the ambulance approaches and lower after it passes.
- Faster velocities or shorter distances make the frequency shift more abrupt.
- The same principle applies to trains, cars, and even light waves in astronomy (e.g., redshift and blueshift).
