The Vespertilionidae family of bats detects the distance to anobject by timing h

Question

The Vespertilionidae family of bats detects the distance to anobject by timing how long it takes for an emitted signal to reflectoff the object and return. Typically the bats emit sound pulses 3ms long and 70 ms apart while cruising. For the purposes of thisquestion, assume that the bat is stationary. (a) If an echo isheard 60 ms later (vsound = 331 m/s), how far away is the object?(b) When an object is only 30 cm away, how long will it be beforethe echo is heard? (c) Will the bat be able to detect thisecho?

Explanation / Answer

Distance equals velocity times time: d = v t However, the sound must travel to the object and back, so the totaldistance is twice the object distance d = 2x Hence, 2x = v t, where x is the distance of the object from thebat (a) v = 331 m/s t = 0.06 s x = v t/2 (b) x = 0.3 m Using the same equation, t = 2x/v If this answer is less than 30 ms (0.03 s), the echo will returnbefore the bat has even finished producing the sound, andtherefore, the bat won't hear it.

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