Final answer:
The frequency of a train whistle being observed by a stationary person as the train approaches at 50 m/s is higher than the initial 1500 Hz posted frequency due to the Doppler effect. To calculate the precise frequency, the Doppler shift formula is applied. Given that the speed of sound is around 343 m/s at room temperature, the frequency observed will be greater than the emitted frequency of 1500 Hz.
Step-by-step explanation:
The question asks about the frequency of a whistle sound from a moving train as perceived by a stationary observer. This is a classic example of the Doppler effect, which describes the change in frequency of a wave in relation to an observer who is moving relative to the wave source. In the case of a train moving towards you at a speed of 50 m/s and emitting a whistle sound of 1500 Hz, the observed frequency, or the pitch you hear, will be higher than the emitted frequency due to the train's approach.
To calculate the actual frequency heard by the stationary observer, we use the formula for the Doppler effect when a source is approaching an observer:
f' = f ( (v + v0) / (v - vs) )
Where:
- f' is the observed frequency
- f is the source frequency (1500 Hz)
- v is the speed of sound (approximately 343 m/s at 20 degrees Celsius)
- v0 is the speed of the observer (0 m/s since the observer is stationary)
- vs is the speed of the source (50 m/s, the speed of the train)
Substituting the values and solving the equation (assuming sound travels at 343 m/s), the observer will hear a higher frequency than 1500 Hz.