A bat, flying at 5.1 m/s, pursues an insect that is flying at 1.1 m/s in the same direction. The bat emits a 47000-Hz sonar pulse. Take the speed of sound to be 343 m/s. show answer No Attempt At what frequency, in hertz, does the bat hear the pulse reflected back from the insect? f = | sin() cos() tan() cotan() asin() acos() atan() acotan() sinh() cosh() tanh() cotanh() Degrees Radians π ( ) 7 8 9 HOME E ↑^ ^↓ 4 5 6 ← / * 1 2 3 → + - 0 . END √() BACKSPACE DEL CLEAR Grade Summary Deductions 0% Potential 100% Submissions Attempts remaining: 3 (4% per attempt) detailed view Hints: 4% deduction per hint. Hints remaining: 2 Feedback: 5% deduction per feedback.

The frequency of the sona-pulse reflected back is  

Explanation:

From the question we are told that

     The speed of the bat is  

      The speed of the insect is

       The frequency emitted by the bat is

        The speed of sound is  

Let look at this question in this manner

At the first instant the that the bat  emits the sonar pulse

     Let the bat be the source of sound

      Let the insect be the observer

This implies that the frequency of sound the the insect would receive is mathematically represented as

Substituting values

Now at the instant the sonar pules reaches the insect

            Let the bat be the observer

            Let the insect be the source of the sound

Here the sound wave is reflected back to the bat

This implies that the frequency of sound the the bat  would receive is mathematically represented as

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west