Doppler Effect of a security alarm

In summary, the security alarm on a parked car produces a frequency of 735 Hz, and as you drive towards and away from it, you observe a change in frequency of 78.4 Hz. Using the formula f=fo*[(V+Vo)/V], the speed of the car can be calculated to be 36 m/s. It appears that the initial attempt at solving this problem resulted in an answer twice the correct value.
  • #1
adashiu
21
0

Homework Statement



The security alarm on a parked car goes off and produces a frequency of 735 Hz. The speed of sound is 343 m/s. As you drive toward this parked car, pass it, and drive away, you observe the frequency to change by 78.4 Hz. At what speed are you driving?

2. The attempt at a solution

Is it correct : ??

fo=735
f=735+78,4=813,4Hz

f=fo*[(V+Vo)/V]
v=36m/s
 
Physics news on Phys.org
  • #2
As you drive towards the stationary car the alarm frequncy is higher due to your movement.
As you go away from it the frequency is lower.
78.4Hz is the difference between these two frequencies.

Without actually doing the working it looks like you've found an answer twice the correct one.
 
  • #3



Your attempt at a solution is partially correct. The equation you used, f = fo * [(V+Vo)/V], is a correct representation of the Doppler effect, where f is the observed frequency, fo is the original frequency, V is the speed of sound, and Vo is the velocity of the observer (in this case, the car). However, you have made a mistake in your calculation. The correct solution is:

fo = 735 Hz
f = 813.4 Hz
V = 343 m/s

813.4 = 735 * [(343+Vo)/343]
1.107 = (343+Vo)/343
Vo = 1.107*343 - 343
Vo = 36.01 m/s

Therefore, you are driving at a speed of 36.01 m/s toward the parked car.
 

1. What is the Doppler Effect?

The Doppler Effect is a phenomenon in which the frequency of a wave appears to change when the source of the wave is moving relative to the observer. It is commonly experienced with sound waves, such as the change in pitch of a siren as an ambulance drives by.

2. How does the Doppler Effect relate to security alarms?

The Doppler Effect can be used in security alarms to detect movement. When an object moves towards or away from the alarm, the frequency of the sound waves it emits will change, triggering the alarm. This is commonly used in motion detectors for home security systems.

3. What factors can affect the accuracy of a security alarm using the Doppler Effect?

The accuracy of a security alarm using the Doppler Effect can be affected by various factors, such as the speed and direction of the moving object, the distance between the object and the alarm, and any obstacles that may interfere with the sound waves.

4. Are there any limitations to using the Doppler Effect in security alarms?

Yes, there are some limitations to using the Doppler Effect in security alarms. For example, the alarm may not be able to detect very slow movements or movements that are parallel to the direction of the sound waves. Additionally, changes in temperature and humidity can also affect the accuracy of the alarm.

5. How can the Doppler Effect be used in other security measures?

The Doppler Effect is not only used in security alarms, but also in other security measures such as radar systems. It is also used in speed guns to detect the speed of moving vehicles. Additionally, it has applications in medical imaging, weather forecasting, and astronomy.

Similar threads

  • Introductory Physics Homework Help
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
7
Views
2K
  • Introductory Physics Homework Help
Replies
22
Views
5K
  • Introductory Physics Homework Help
Replies
1
Views
5K
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
1K
Back
Top