Final answer:
The perceived pitch is lower as the train moves away due to the Doppler effect. Using the given observed frequency of 305 Hz and the speed of the train as 50.0 m/s, the actual frequency is calculated to be approximately 351 Hz.
Step-by-step explanation:
As the train moves away from you, the perceived pitch of the train's horn would be lower than the actual frequency of the horn. This phenomenon is explained by the Doppler effect, which describes the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source. In this case,
since the train (the source of the sound) is moving away from the observer, the waves are stretched, resulting in a lower frequency heard by the observer.
To calculate the actual frequency of the train's whistle as it recedes, you would use the Doppler effect equation: f' = f * (v + vo) / (v + vs), where f' is the observed frequency, f is the actual frequency, v is the speed of sound, vo is the speed of the observer, and vs is the speed of the source.
Since the observer is stationary (vo = 0 m/s) and the train is moving away (vs is positive), we can rewrite the equation as f' = f * v / (v + vs).
Given the problem states you hear a frequency of 305 Hz as the train recedes, and given the speed of the train is 50.0 m/s with the speed of sound approximated at 331 m/s, we can solve for f as follows:
- Identify known: f' = 305 Hz, vs = 50.0 m/s, v = 331 m/s.
- Plug the values into the equation: 305 = f * 331 / (331 + 50).
- Solve for f: f = 305 * (331 + 50) / 331.
- Calculate the actual frequency: f is approximately 351 Hz.
Thus, the actual frequency of the whistle as the train moves away is approximately 351 Hz.