A light-rail commuter train blows its 200 Hz horn as it approaches a crossing. The speed of sound is 330 m/s.
To determine the frequency of the train's horn as heard by an observer, we need to take into account the concept of Doppler Effect. The Doppler Effect explains the change in frequency of a wave (sound, light, etc.) perceived by an observer due to the relative motion between the source of the wave and the observer.
In this case, the frequency of the horn provided is 200 Hz. However, we need to calculate the observed frequency as heard by a stationary observer, assuming the train is approaching the observer.
To do this, we can use the following formula for the Doppler Effect with sound:
Observed frequency = Source frequency × (Speed of sound + Speed of observer) / (Speed of sound + Speed of source)
In this case, the source frequency is 200 Hz, and the speed of sound is given as 330 m/s. However, we need to determine the speed of the observer (in this case, the stationary person), and the speed of the source (the train).
Since the problem statement doesn't mention the speed of the train or the observer, we can assume the observer is stationary (speed = 0). Therefore, the formula simplifies to:
Observed frequency = Source frequency × Speed of sound / (Speed of sound + Speed of source)
Now, we can substitute the given values:
Observed frequency = 200 Hz × 330 m/s / (330 m/s + Speed of source)
To solve this equation, we need to know the speed of the train.