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

[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.

 

[RPinPA]

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 $v$.