Horseshoe bats (genus Rhinolophus) emit sounds from their nostrils, then listen to the frequency of the sound reflected from their prey to determine the prey's speed. The horse shoe that gives the bat its name is a depression around the nostrils that acts like a focussing mirror so that the bat emits sound in a narrow beam like a flash light. A Rhinolophus is flying at a speed $v_{b a t}$ and enits sound of frequency $f_{b a t}$ the sound it hears reflected from an insect flying towards it has higher frequency $f_{r e f}$ , speed sound is $v_{s}$ If $f_{b a t} = 80.7$ kHz, $f_{r e f} = 83.5$ kHz and $v_{i n s e c t} = 2 m s^{- 1}$ . Find $v_{b a t}$ :

4.9 m s^{- 1}

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3.9 m s^{- 1}

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5.9 m s^{- 1}

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4.1 m s^{- 1}

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Solution

The correct option is B $3.9 m s^{- 1}$
$f_{1} = f_{b a t} \frac{V_{s} + V_{i n}}{V_{s} - V_{b a t}}$
and $f_{r e f} = f_{1} \frac{V_{s} + V_{b a t}}{V_{s} - V_{i n}}$

$\frac{f_{r e f}}{f_{b a t}} = \frac{(V_{s} + V_{i n}) (V_{s} + V_{b a t})}{(V_{s} - V_{i n}) (V_{s} - V_{b a t})}$

or $\frac{83.5}{80.7} = \frac{(340 + 2) (340 + V_{b a t})}{(340 - 2) (340 - V_{b a t})}$

or $1.03 = \frac{342 \times (340 + V_{b a t})}{338 \times (340 - V_{b a t})}$

or $1.022 = \frac{(340 + V_{b a t})}{(340 - V_{b a t})}$

or $V_{b a t} = 3.9 m / s$

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Similar questions

v_{b a t}

f_{b a t}

f_{r e f}

v_{s}

v_{i n s e c t}

100 kHz

340 {ms}^{- 1}

100 kHz

= 340 {ms}^{- 1}

= 1500 {ms}^{- 1}

39000 Hz

0.025

100 k H z

340 m s^{- 1}

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