A train is moving at a speed of 30 m/s toward a stationary observer at a train station. The train whistle blows with an actual frequency of 336 Hz.
What horn frequency is heard by the engineer (riding on the train)?
336
To determine the horn frequency heard by the engineer riding on the train, we need to consider the phenomenon of Doppler effect. The Doppler effect refers to the change in frequency of a wave (in this case, sound) due to the relative motion between the source of the wave (the train) and the observer (the engineer).
In this situation, the train is moving towards the observer (the train station). As a result, the sound waves emitted by the train's horn are compressed or "bunched up" as they reach the engineer. This compression increases the apparent frequency of the sound heard by the engineer.
To calculate the horn frequency heard by the engineer, we can use the following formula:
f_observed = f_actual * (v_sound + v_observer) / (v_sound + v_source)
Where:
- f_observed is the frequency heard by the observer (in this case, the engineer)
- f_actual is the actual frequency of the sound (in this case, 336 Hz)
- v_sound is the speed of sound in air (approximately 343 m/s at 20 degrees Celsius)
- v_observer is the velocity of the observer (in this case, the stationary observer at the train station)
- v_source is the velocity of the source (in this case, the velocity of the train)
Since the observer is stationary (v_observer = 0), and the train is moving towards the observer (v_source = -30 m/s), we can substitute these values into the formula:
f_observed = 336 Hz * (343 m/s + 0 m/s) / (343 m/s - (-30 m/s))
Simplifying the equation, we get:
f_observed = 336 Hz * (343 m/s) / (373 m/s)
Calculating the values, we find:
f_observed ≈ 308.2 Hz
Therefore, the horn frequency heard by the engineer riding on the train is approximately 308.2 Hz.