A patrol car is moving at a constant speed towards a stationary observer - NSC Physical Sciences - Question 6 - 2019 - Paper 1

The Doppler effect refers to the change in frequency (or pitch) of a wave in relation to an observer who is moving relative to the wave source. When the source approaches the observer, the frequency increases, and when it moves away, the frequency decreases.

The detected frequency changes at t = 10 s because this is the moment when the patrol car passes the observer. At this point, the source of the sound (the siren) is moving directly away from the observer, resulting in a decrease in the detected frequency.

We can use the Doppler effect formula to find the frequency of the sound emitted by the siren:

$f_t = \frac{v + v_o}{v - v_s} f_s$

For a stationary observer ( v_o = 0), the equation simplifies to:

$f_t = \frac{v}{v - v_s} f_s$

At the point where the detected frequency is 932 Hz when approaching, and $v = 340$ m/s. We can rearrange to find $f_s$:

$932 = \frac{340}{340 - 30} f_s$

Solving gives:

$f_s = 932 \times \frac{340 - 30}{340} = 849.76 \text{ Hz}.$

Thus, the frequency of the sound emitted by the siren is approximately 849.76 Hz.

1. Radar and sonar systems are often used to determine the speed of objects, such as vehicles or fish, by analyzing the frequency changes of reflected waves.

2. The Doppler effect can also be utilized in astronomy to determine whether stars or galaxies are moving towards or away from Earth, by observing changes in the frequency of light from those objects.