Question

An observer is standing next to the tracks, watching a train approach. The train travels at 30 m/s and blows its whistle at 8,000 Hz as it approaches and then passes by the observer without slowing down. Assuming the speed of sound is 340 m/s, how much of a frequency change did the observer hear?

Answer 1

The observer hears a frequency change due to the Doppler effect. The observed frequency can be calculated using the formula fobs = fs * vw / (vw ± vs). When the train approaches, the observer hears a frequency of 7226.63 Hz, and when it moves away, the observer hears a frequency of 8791.83 Hz.

Step-by-step explanation:

The observer hears a change in frequency due to the Doppler effect when the train approaches and passes by. The formula for calculating the observed frequency is:

fobs = fs * (vw / (vw ± vs))

Where:

• fobs is the observed frequency
• fs is the source frequency
• vw is the velocity of the wave (speed of sound)
• vs is the velocity of the source (train)

Using the given values:

• fs = 8000 Hz
• vw = 340 m/s
• vs = 30 m/s

Substituting the values into the formula:

fobs = 8000 Hz * (340 m/s / (340 m/s ± 30 m/s))

Simplify the formula by calculating both cases, when the train approaches and when it moves away:

When approaching: fobs = 8000 Hz * (340 m/s / (340 m/s + 30 m/s))

When moving away: fobs = 8000 Hz * (340 m/s / (340 m/s - 30 m/s))

Calculating the values:

• When approaching: fobs = 7226.63 Hz
• When moving away: fobs = 8791.83 Hz

Therefore, the observer hears a frequency change of approximately 7226.63 Hz when the train approaches and 8791.83 Hz when it moves away.