Final answer:
Using the Doppler Effect, the frequency observed by the bank robber for the siren of the police car chasing at different speeds would be approximately 500 Hz, taking into account the relative motion of both the observer and the source.
Step-by-step explanation:
To determine the frequency that the bank robber would observe from the police car's siren, we employ the Doppler Effect. The formula for the Doppler Effect when the source is moving toward the observer is:
f' = f * (v + vo) / (v - vs)
Where:
- f' is the observed frequency.
- f is the emitted frequency (400 Hz in this case).
- v is the speed of sound in air (we will use 343 m/s as a standard value).
- vo is the speed of the observer (the bank robber, who is moving at 30 m/s).
- vs is the speed of the source (the police car, moving at 60 m/s).
Plugging in the values, we get:
f' = 400 Hz * (343 m/s + 30 m/s) / (343 m/s - 60 m/s)
f' = 400 Hz * (373 m/s)/(283 m/s)
f' = 402.2 Hz
However, since the bank robber is also moving, we must consider this in our calculation. The adjusted observed frequency will be slightly higher than the stationary observed frequency. Given the options provided, the closest value would be 500 Hz (C), as the choice needs to reflect the change due to the relative speeds of the source and the observer.