Question

A mechanical high-speed bat is flying along a path perpendicular to a wall. it emits a sound with a frequency f0 . the night is clear and the air is still. let the speed of sound waves in the still air be vs . the bat hears a sound wave reflected from the wall with a frequency fnew . from this information one can determine the speed vbat at which the bat is flying. install a detector at the wall. 0 bat f v what is the detected frequency? 1. f1 = vs + vbat vs f0 2. f1 = vs vs − vbat f0 3. f1 = vs vs + vbat f0 4. f1 = vs + vbat vs − vbat f0 5. f1 = 2 vs vs − vbat f0 6. f1 = vs − vbat vs f0 7. f1 = vs − vbat vs + vbat f0 8. f1 = f0 9. f1 = 2 vs vs + vbat f0

Answer 1

1. f1 = Vs + Vbat Vs fO
2. f1 = Vs Vs - Vbat fO
3. f1 = Vs Vs + Vbat fO
4. f1 = Vs + Vbat Vs - Vbat fO
5. f1 = 2Vs Vs - Vbat fO
6. f1 = Vs - Vbat Vs fO
7. f1 = Vs - Vbat Vs + Vbat fO
8. f1 = fO
9. f1 = 2Vs Vs + Vbat fO

The observed frequency is
f= (V+Vr) × fO/ (V + Vs)
The speed of the sound is V = Vs
The speed of the receiver is  Vr = O
The speed of the source
Vs = -Vbat where negative is the bat which is approaching the wall
Then the correct answer is 
f1 = (Vs / (Vs -Vbat)) × fO.