Final answer:
Using the Doppler effect, we can calculate the speed of a train based on the change in frequency of the sound it emits. A 30 dB increase in sound intensity represents a significant increase in loudness. The train speed and resulting frequencies for an approaching and departing train can be determined using physics principles.
Step-by-step explanation:
When a train approaches a crossing and emits a signal, the frequency of this signal as heard by an observer can change due to the Doppler effect. This effect explains the change in frequency or wavelength of a wave in relation to an observer moving relative to the source of the wave. If an observer waiting at a crossing receives a frequency of 208 Hz while the train horn was originally emitting a 200 Hz sound, we can calculate the speed of the train using the formula derived from the Doppler effect.
For the sound intensity level concern, a difference of 30 decibels (dB) represents a significant increase in perceived loudness. The logarithmic scale of decibels means that every 10 dB increase is perceived as a doubling of loudness. Therefore, if the sound intensity level will increase from 70 dB to 100 dB as a result of the new train service, the townspeople will likely experience a drastic increase in loudness, which can be a cause for concern.
(a) To calculate the train's speed, we can apply the Doppler effect formula.
(b) As the train moves away, the frequency perceived will decrease below the original 200 Hz due to the source moving away from the observer. The exact new frequency can also be calculated using the same principles.