A bat is flying at velocity vb. The bat emits a sound wave with frequency f. The sound wave reflects from a stationary object, and the bat hears the reflected sound. What frequency f′ does the bat hear? In the expressions below, vs is the speed of the source, vo is the speed of the observer, and v is the speed of sound. (In this case, the bat is both the source and the observer, so that |vs| = |vo| = |vb|.)
1) f′ =f1+|vo/v| 1 + |vs/v|
2) f′ =f1-|vo/v| 1 + |vs/v|
3) f′ =f1+|vo/v| 1 - |vs/v|
4) f′ =f1-|vo/v| 1 - |vs/v|