Help with doppler problem thanks

[kle89]

A student runs toward the closed end of a hall while holding a vibrating tuning fork. The tuning fork is vibrating at 512Hz. The sound is reflected from the end of the hall back to the running student where 8.0 beats per second can be heard. Determind the speed of the student.

i used the equation f' = f [(v +/- vo)/(v +/- vs)]

8 = 512 [(343 +/- 0)/(343 +/- vs)]

and tried solving for vs to get the speed of the student, however the answer i got differed from what the teacher gave us, which was 2.6 m/s. I got 21609. Am i using the right equation?

 

[turdferguson]

8 beats per second means that the difference in frequencies is 8 Hz

 

[Dick]

You are doing one thing very wrong. 8 beats per minute is not f'. Its the frequency difference between f and f'. So put f'=512+8. There is also a factor of two missing. Its not a doppler problem between a moving observer and a static receiver. So vo should not be zero. In fact, vo should be -vs. The picture you should have is a student running towards a mirror. Its the same as though you had two students running towards each other. I'm sorry if this is confusing - its confusing for me as well, but I don't know how to explain it better.