Two identical cars are moving — one toward you and the other away from you. The cars
are both travelling at 6.0 m/s. Each car has a horn that produces a 525-Hz tone when at rest.
Assume that the speed of sound is 344 m/s. What frequency will you hear from each car?
What will you hear when the frequencies are combined?
To determine the frequency you will hear from each car, we need to use the concept of Doppler effect, which states that the observed frequency of a wave changes when there is relative motion between the source of the wave and the observer.
For the car moving towards you:
The observed frequency, denoted as f_obs, is given by the equation:
f_obs = (v_sound + v_observer) / (v_sound + v_source) * f_source
In this case, the speed of sound (v_sound) is 344 m/s, the speed of the observer (you) is 0 m/s since you are stationary, and the speed of the source (car moving towards you) is -6.0 m/s (negative because it is moving towards you).
Plugging these values into the equation, we have:
f_obs_towards = (344 + 0) / (344 - 6.0) * 525 Hz
Now, let's calculate:
f_obs_towards = 350.46 Hz
So, the frequency you will hear from the car moving towards you is approximately 350.46 Hz.
For the car moving away from you:
The observed frequency, denoted as f_obs, is given by the equation:
f_obs = (v_sound - v_observer) / (v_sound - v_source) * f_source
In this case, the speed of sound (v_sound) is 344 m/s, the speed of the observer (you) is 0 m/s, and the speed of the source (car moving away from you) is +6.0 m/s.
Plugging these values into the equation, we have:
f_obs_away = (344 - 0) / (344 + 6.0) * 525 Hz
Now, let's calculate:
f_obs_away = 511.43 Hz
So, the frequency you will hear from the car moving away from you is approximately 511.43 Hz.
When the frequencies are combined, you will hear the sum of the frequencies. Therefore, the combined frequency will be:
f_combined = f_obs_towards + f_obs_away
Plugging in the calculated values, we get:
f_combined = 350.46 Hz + 511.43 Hz
Now, let's calculate:
f_combined = 861.89 Hz
So, when the frequencies are combined, you will hear a sound with a frequency of approximately 861.89 Hz.