Question

Bats of the Vespertilionidae family detect the distance to an object by timing how long it takes for an emitted signal to reflect off the object and return. Typically they emit sound pulses 3.00 ms long and 70.0 ms apart while cruising.

If an echo is heard 30.6 ms later (v_sound = 331 m/s), how far away is the object?

When an object is only 41.7 cm away, the bat  (Click to select)  will not be, will be, ) able to detect the echo.

Answer 1

Incident sound wave Reflected sound wave obstacle

From the above diagram

let us consider that distance covered by incedent sound wave = x cm

thus total distance(incident + reflected) will be = 2x cm

Given

1. time taken to hear echo = 30.6 ms = 0.0306 s

2. velocity of sound (v) = 331 m/s

We know that

  $velocity(v) =\tfrac{distance(2x)}{time(t)}$

thus

$x =\tfrac{vt}{2}$   

$x =\tfrac{331\times 0.0306}{2}$

  x = 5.0643 m

thus

Object is 5.0643 m away from Bat.