C.5 Doppler Effect SL Paper 1- IBDP Physics 2025- Exam Style Questions

Ans C

(First Shift)

The car moves toward the radar detector with speed \( v \), and the radar emits microwaves of frequency \( f \) and speed \( c \).
The frequency received by the moving car is given by the Doppler formula

$
f’ = f \left(\frac{c + v}{c}\right)
$

where:
\( f’ \) is the frequency detected by the moving car.
\( c \) is the speed of light.

Since the car is moving toward the source, the frequency increases.

(Second Shift)
The moving car acts as a new source, reflecting the frequency \( f’ \) back to the detector.
 the detector is stationary and the car is moving toward it, another Doppler shift occurs

$
f” = f’ \left(\frac{c + v}{c}\right)
$

$
f” = f \left(\frac{c + v}{c}\right) \times \left(\frac{c + v}{c}\right)
$

$
f” = f \left(\frac{(c + v)^2}{c^2}\right)
$

Expanding for small \( v/c \), using approximation \( (1 + x)^2 \approx 1 + 2x \) for small \( x \)

$
f” \approx f \left(1 + \frac{2v}{c}\right)
$

$
\Delta f = f” – f = f \frac{2v}{c}
$