# How to Solve a Doppler Effect Problem with a Moving Vehicle and Siren at Rest

• jariz
In summary, the conversation discusses a problem involving the calculation of wavelength using the formula wavelength = velocity/frequency. However, there seems to be an error in the given information, as the vehicle is moving at the start and the siren is not at rest. The suggested solution is to use a variable to represent the unknown speed of the vehicle and solve the problem in terms of that variable.

#### jariz

Homework Statement
Two students (A and B) hear a siren from an emergency vehicle, heading East along Rivers St with a speed of 10.0 kHz. Student A is standing still on the sidewalk, while Student B is jogging West, with a speed of 6.20 m/s. The vehicle starts 300 m away from the students and continues past them, for the purposes of this problem.

Find the frequencies heard by Student A, As the vehicle approaches the student.
When the vehicle and student are side-by-side.
As the vehicle moves away from the student.

Repeat the above items for Student B.

I believe I could figure this out fairly easily if I could just get the velocity of the emergency vehicle. I have never seen the speed represented in kHz and as I don't know the wavelength, I don't know how to calculate velocity from velocity = wavelength*frequency. Maybe I'm going about this all wrong, but I'm struggling just to get started on this problem. Any help at all would be appreciated.
Relevant Equations
Wavelength = velocity/frequency. Speed of sound = 343 m/s.
Pretending the siren is at rest in air:
Wavelength = velocity/frequence --> (343 m/s) / 10,000 Hz = .0343m.

I don't believe this is the correct way to go about solving the problem, since the vehicle is moving at the start and the siren is not at rest.

Yeah, that's an error. I suspect the original sentence said the emitted frequency was 10.0 kHz and that it also gave a speed. Something got accidentally deleted.

About all you can do, barring a correction from the teacher, is use a variable ##v## to represent the (unknown) speed of the vehicle and then solve the problem in terms of ##v##.

jariz

## 1. How does the Doppler effect work in a moving vehicle with a siren at rest?

The Doppler effect is a phenomenon that occurs when there is a relative motion between a source of sound and an observer. In the case of a moving vehicle with a siren at rest, the sound waves from the siren will be compressed in front of the vehicle and stretched behind it due to the vehicle's motion. This results in a change in the perceived frequency of the sound, which is known as the Doppler effect.

## 2. How do I calculate the frequency of the sound heard by an observer in a moving vehicle?

The frequency of the sound heard by an observer in a moving vehicle can be calculated using the formula: f' = f(v ± vr)/(v ± vs), where f is the frequency of the sound emitted by the siren, v is the speed of sound, vr is the relative velocity of the vehicle and the observer, and vs is the speed of the vehicle.

## 3. What is the difference between the "Approaching" and "Receding" cases in a Doppler effect problem?

In the "approaching" case, the observer is moving towards the source of the sound, resulting in a higher perceived frequency due to the compression of the sound waves. In the "receding" case, the observer is moving away from the source of the sound, resulting in a lower perceived frequency due to the stretching of the sound waves.

## 4. Can the Doppler effect be observed with other types of waves besides sound waves?

Yes, the Doppler effect can be observed with any type of wave, including light waves and water waves. In these cases, the observed frequency is affected by the relative motion between the source and the observer.

## 5. How can the Doppler effect be used in real-world applications?

The Doppler effect has many practical applications, such as in radar and sonar systems, where it is used to determine the speed and direction of moving objects. It is also used in medical imaging techniques, such as ultrasound, to create images of internal structures in the body. Additionally, the Doppler effect is used in astronomy to measure the speed and direction of distant objects in space.