Final answer:
The apparent frequency heard by a passenger due to the Doppler effect when a truck approaching at 30.0 m/s with a 150 Hz horn meets an oncoming car at 35.0 m/s is approximately 181.15 Hz.
Step-by-step explanation:
The student's question involves calculating the apparent frequency heard by a passenger in a car due to the Doppler effect when a truck approaches the car. The Doppler effect describes the change in frequency (or wavelength) of a wave in relation to an observer who is moving relative to the wave source. To calculate the apparent frequency the passenger hears, we need to use the Doppler effect formula:
f' = f ( v + vo ) / ( v - vs )
Where:
- f' is the apparent frequency received by the observer,
- f is the source frequency (150 Hz),
- v is the speed of sound (which we can assume at 20°C to be approximately 343 m/s),
- vo is the speed of the observer (35.0 m/s toward the source),
- vs is the speed of the source (30.0 m/s toward the observer).
Inserting the given values into the equation, we get:
F' = 150 Hz (343 m/s + 35.0 m/s) / (343 m/s - 30.0 m/s)
F' = 150 Hz (378 m/s) / (313 m/s)
Now, we simplify and calculate the apparent frequency:
F' ≈ 150 Hz × 1.20767
F' ≈ 181.15 Hz
Therefore, the startled passenger in the car would hear an apparent frequency of approximately 181.15 Hz.