133k views
2 votes
A large truck travelling at 30.0 m/s sounds its 150 Hz horn to warn an on coming car traveling at 35.0 m/s . what would be the apparent frequency to a startled passenger in the car if the temperature is 20C ?

1 Answer

1 vote

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.

User Whitneyit
by
8.2k points