A light-rail commuter train blows its 200 Hz horn as it approaches a crossing. The speed of sound is 332 m/s.
Incomplete.
To find the observed frequency of the horn as heard by an observer at the crossing, we need to consider the Doppler effect. The Doppler effect occurs when there is relative motion between the source of a wave (in this case, the moving train) and the observer (at the crossing).
The observed frequency, denoted as f', can be calculated using the equation:
f' = f * (v + v₀) / (v + v₁)
Where:
f is the original frequency of the horn (200 Hz in this case)
v is the speed of sound (332 m/s)
v₀ is the speed of the observer(in this case, assumed to be zero, as the observer is stationary)
v₁ is the speed of the source (the train)
Since the train is approaching the observer at the crossing, its speed relative to the observer is positive. Thus, v₁ would be positive.
Plugging in the values, we have:
f' = 200 Hz * (332 m/s + 0 m/s) / (332 m/s + v₁)
Simplifying, we get:
f' = 200 Hz * 332 m/s / (332 m/s + v₁)
The observed frequency will depend on the speed of the train relative to the observer.