Doppler Effect; Two Moving Objects

In summary, the problem involves two cars driving towards each other at different speeds. The frequency of the horns of both cars is given as 524 Hz. Using the Doppler effect formula for a moving source and a moving observer, the frequency heard by each driver can be calculated as 593 Hz and 594 Hz respectively.
  • #1
MAtkinson
4
0

Homework Statement



Two auto-mobiles are driving on the same road in opposite directions. The speed of the first auto-mobile is 90.0 km/h and that of the second is 60 km/h. The horns of both auto-mobiles emit tons of frequency 524 Hz. Calculate the frequency that the driver of each auto-mobile hears coming from the other auto-mobile.

Homework Equations



Doppler Effect

1. For a Moving Source and Stationary Object
f=fv/(v-vsource)

The Attempt at a Solution



Car one (90km/h) is moving 30 km/h toward the other.

f=524*340/(340-30)



Answer {593Hz, 594Hz}
 
Physics news on Phys.org
  • #2
MAtkinson said:
Car one (90km/h) is moving 30 km/h toward the other.
How did you arrive at this?

Both cars are moving with respect to the road (and air) towards each other. You also need to revise your formula, since both observer and source are moving.
 
  • #3
Wow never-mind that statement it would the cars would appear to be moving 150 km/h toward each other. But I'm still confused on how to setup the Doppler effect.
 
  • #4
MAtkinson said:
Wow never-mind that statement it would the cars would appear to be moving 150 km/h toward each other. But I'm still confused on how to setup the Doppler effect.
Don't worry about their relative speed, but their speeds with respect to the ground/air. Just like there's a Doppler formula for a moving source, there's one for a moving observer. Here both source and observer are moving, so you must combine both formulas.
 
  • #5


I would like to clarify that the Doppler Effect is a phenomenon in which the perceived frequency of a wave changes when there is relative motion between the source of the wave and the observer. In this case, the two automobiles are both sources and observers, and their relative motion causes a change in the frequency of the sound waves emitted by their horns.

Using the equation provided in the homework, we can calculate the frequency that each driver hears from the other automobile. For car one, which is moving towards the other car at a speed of 30 km/h, the frequency heard would be slightly higher than the emitted frequency of 524 Hz. This can be calculated as follows:

f1 = (524 Hz) * (340 m/s) / (340 m/s - 30 km/h * 1000 m/km / 3600 s/h)
f1 = 524.58 Hz

Similarly, for car two, which is moving away from the other car at a speed of 60 km/h, the frequency heard would be slightly lower than the emitted frequency of 524 Hz. This can be calculated as follows:

f2 = (524 Hz) * (340 m/s) / (340 m/s + 60 km/h * 1000 m/km / 3600 s/h)
f2 = 523.41 Hz

Therefore, the driver of car one would hear a frequency of approximately 524.58 Hz coming from car two, while the driver of car two would hear a frequency of approximately 523.41 Hz coming from car one. This slight difference in frequency is due to the Doppler Effect and the relative motion between the two cars.
 

1. What is the Doppler Effect?

The Doppler Effect is the change in frequency or wavelength of a wave for an observer who is moving relative to the wave source. It is most commonly observed with sound waves, but it can also occur with other types of waves, such as light waves.

2. How does the Doppler Effect work?

The Doppler Effect works by changing the perceived frequency of a wave as the source of the wave and the observer are in motion relative to each other. When the source is moving towards the observer, the frequency appears higher, and when the source is moving away from the observer, the frequency appears lower.

3. How does the Doppler Effect apply to two moving objects?

In the case of two moving objects, the Doppler Effect is observed when both objects are in motion relative to each other. The frequency of the waves emitted by one object will appear to be higher or lower to the other object depending on their relative motion.

4. What is the formula for calculating the Doppler Effect for two moving objects?

The formula for calculating the Doppler Effect for two moving objects is f' = f(v ± vr) / (v ± vs), where f' is the perceived frequency, f is the emitted frequency, v is the speed of the wave, vr is the relative velocity between the two objects, and vs is the velocity of the source.

5. How is the Doppler Effect used in real life?

The Doppler Effect has many practical applications in real life. It is used in radar and sonar systems to determine the velocity of objects, in medical imaging techniques to measure blood flow, and in astronomy to study the motion of stars and galaxies. It is also used in everyday technologies such as police radar guns and speed cameras.

Similar threads

  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
7
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
10
Views
6K
Back
Top