Final answer:
Using the Doppler effect formula, the perceived frequency by the truck driver in front of the fire engine, both moving in the same direction with respective speeds of 20 m/s and 30 m/s, is calculated to be approximately (c) 2020 Hz.
Step-by-step explanation:
The question involves the calculation of perceived frequency due to the Doppler effect, which occurs when there is relative motion between a source of sound and an observer. The formula we apply here takes into account the speeds of both the observer and the source, as well as the speed of sound in the medium.
To find the frequency heard by the truck driver in front of the fire engine, we use the formula:
f' = f (v + vo) / (v + vs)
Where:
- f' is the frequency perceived by the observer.
- f is the emitted frequency of the source (2000 Hz).
- v is the speed of sound in air (assumed here to be 343 m/s for a typical air temperature).
- vo is the velocity of the observer (the truck moving at 20 m/s).
- vs is the velocity of the source (the fire engine, moving at 30 m/s).
The speed of the truck (the observer) and the fire engine (the source) are both in the direction of the sound wave, which means they are added to the speed of sound in the numerator and subtracted from the denominator respectively. Once we plug in these values:
f' = 2000 Hz (343 m/s + 20 m/s) / (343 m/s + 30 m/s)
Solving this equation gives us the perceived frequency which comes out to approximately 2020 Hz, which is option c).