A train is moving parallel to a highway with a constant speed of 16.0 m/s. A car is traveling in the same direction as the train with a speed of 36.0 m/s. The car horn sounds at a frequency of 504 Hz, and the train whistle sounds at a frequency of 314 Hz.
(a) When the car is behind the train, what frequency does an occupant of the car observe for the train whistle?
Hz
(b) After the car passes and is in front of the train, what frequency does a train passenger observe for the car horn?
Hz
when the car is behind the train, the listener in the car is approaching the sound source in the train at 36-16 = 20 m/s
The listener will hear a higher frequency.
when the car is ahead of the train, the listener in the train is departing from the sound source in the car at 20 m/s and will hear a lower frequency.
In general:
Fl = frequency listener
Fs = frequency source
v = sound speed assume 340 m/s
vl is velocity of listener toward source. It is negative if in direction away from source.
(in part a it is +)
(in part b it is +)
vs is velocity of source. It is negative if opposite to the direction of the listener toward the source
(in part a it is +)
(in part b it is +)
Fl = Fs(v + vl)/(v + vs)
part a
Fcar = Ftrain whistle (340+36)/(340+16)
Fcar = 1.056 Fwhistle
pert b
Ftrain passenger= Fcar (340+16)/(340+36)
Ftrain passenger = .947 F car horn
A train is moving parallel to a highway with a constant speed of 20 m/s. A car is traveling with a speed of 40.0 m/s. The car’s horn sound at a frequency of 510 Hz, and the train whistle sounds at a frequency of 320 Hz. When the car is behind the train, what frequency does an occupant of the car observe for the train whistle?
(a) When the car is behind the train, an occupant of the car will observe a lower frequency for the train whistle. This is known as the Doppler effect. To calculate this, we can use the formula:
Observed frequency = Source frequency × (Speed of sound + Observer's velocity) / (Speed of sound + Source's velocity)
In this case, the source frequency is 314 Hz, the speed of sound is approximately 343 m/s, the observer's velocity is 36.0 m/s (since the car is traveling in the same direction as the train), and the source's velocity is 16.0 m/s. Plugging in the values into the formula, we can calculate:
Observed frequency = 314 Hz × (343 m/s + 36.0 m/s) / (343 m/s + 16.0 m/s)
Simplifying, we get:
Observed frequency ≈ 298 Hz
So when the car is behind the train, an occupant of the car would observe a frequency of approximately 298 Hz for the train whistle.
(b) After the car passes and is in front of the train, a train passenger will observe a higher frequency for the car horn. We can use the same Doppler effect formula to calculate this. In this case, the source frequency is 504 Hz, the speed of sound is approximately 343 m/s, the observer's velocity is -16.0 m/s (since the train is stationary), and the source's velocity is 36.0 m/s (since the car is traveling in the same direction as the train). Plugging in the values into the formula, we can calculate:
Observed frequency = 504 Hz × (343 m/s - 16.0 m/s) / (343 m/s + 36.0 m/s)
Simplifying, we get:
Observed frequency ≈ 558 Hz
So after the car passes and is in front of the train, a train passenger would observe a frequency of approximately 558 Hz for the car horn.
To find the observed frequencies, we'll use the concept of Doppler effect. The Doppler effect is the change in frequency or wavelength of a wave for an observer moving relative to its source.
(a) When the car is behind the train, the car and the train are moving in the same direction. To find the frequency observed by an occupant of the car for the train whistle, we'll use the formula:
\(f' = \frac{{f \cdot (v+ v_o)}}{{v + v_s}}\)
Where,
\(f =\) frequency of the source (train whistle) = 314 Hz
\(v =\) speed of sound = 343 m/s (approximately)
\(v_o =\) speed of the observer (car) = 36.0 m/s
\(v_s =\) speed of the source (train) = 16.0 m/s
Plugging in the values, we get:
\(f' = \frac{{314 \cdot (343 + 36.0)}}{{343 + 16.0}}\)
Simplifying this expression will give us the frequency observed by the car occupant.
(b) After the car passes and is in front of the train, the car and the train are moving in opposite directions. To find the frequency observed by a train passenger for the car horn, we'll use the same formula as above:
\(f' = \frac{{f \cdot (v + v_o)}}{{v - v_s}}\)
Where,
\(f =\) frequency of the source (car horn) = 504 Hz
\(v =\) speed of sound = 343 m/s (approximately)
\(v_o =\) speed of the observer (train passenger) = 0 m/s (since the passenger is stationary)
\(v_s =\) speed of the source (car) = 36.0 m/s
Plugging in the values, we get:
\(f' = \frac{{504 \cdot (343 + 0)}}{{343 - 36.0}}\)
Simplifying this expression will give us the frequency observed by the train passenger.