In each of the four scenarios to the right, a large bat lets out a short burst o

Question

In each of the four scenarios to the right, a large bat lets out a short burst of ultrasonic sound, which the smaller bat hears a moment later. If the large bat flies at 2.650 m/s and the small bat flies at 13.00 m/s, rank the frequency that the smaller bat detects in the four scenarios, from highest to lowest. Assume that the speed of sound is 343.0 m/s. In scenario C, some of the large bat's signal reflects off of the small bat and returns to the large bat, warning it of the smaller bat's presence. If the initial signal has a frequency of 45.50 kHz, what return frequency will the large bat detect? Calculate the final frequency to four significant figures.

Explanation / Answer

Vs = speed of large bat = 2.650 m/s

VL = speed of small bat = 13 m/s

V = speed of sound = 343 m/s

f = frequency f sound by the large bat

f' = frequency heard by small bat

Case A :

large bat is moving in the direction of small bat but VL > Vs

f' = (V - VL) f/(V - Vs) = (343 - 13) f/(343 - 2.650) = 0.97 f

Case B:

bats are moving in opposite direction away from each other

f' = (V - VL) f/(V - Vs) = (343 - 13)) f/(343 - (- 2.650)) = 0.95 f

Case C:

bats are moving in opposite direction towards each other

f' = (V - VL) f/(V - Vs) = (343 - (-13))) f/(343 - (2.650)) = 1.05 f

case D:

f' = (V - VL) f/(V - Vs) = (343 - (-13))) f/(343 - (- 2.650)) = 1.03 f

Ranking :

C >D >A>B

frequency received by small bat is given as

f' = 1.05 f = 1.05 x 45.5 = 47.775 kHz

frequency heard by the large bat is given as

f' = (V - VL) f/(V - Vs) = (343 - (-2.650)) (47.775)/(343 - 13) = 50.04 kHz

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