Final answer:
The apparent frequency of a 2000 Hz train whistle moving towards a stationary observer at 40.0 m/s can be calculated using the Doppler effect formula. Substituting the values into the formula, the apparent frequency is approximately 1777 Hz.
Step-by-step explanation:
The apparent frequency of a train whistle can be calculated using the Doppler effect formula:
f' = (v + vo) / (v + vs) * f
Where:
- f' is the apparent frequency heard by the observer
- v is the speed of sound (331 m/s at 20 C)
- vo is the speed of the observer (0 m/s as they are stationary)
- vs is the speed of the source (40.0 m/s for the train)
- f is the actual frequency of the train whistle (2000 Hz)
Substituting the values:
f' = (331 + 0) / (331 + 40.0) * 2000
Simplifying the equation:
f' = 331 / 371 * 2000
f' ≈ 1777 Hz
Therefore, the apparent frequency of the 2000 Hz train whistle that is moving towards a stationary observer at 40.0 m/s on a 20 C day is approximately 1777 Hz.