Question #f55c0

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Question #f55c0

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Answer 1 · 2017-05-16T21:16:26

$Please examine carefully the animation.$ $"Please examine carefully the animation."$
$The sound emitted by the ambulance is perceived differently$ $"The sound emitted by the ambulance is perceived differently"$
$by the observers.$ $"by the observers."$
$v_{S} = 25.19 \frac{m}{s}$ $v_S=25.19" "m/s$

Explanation:

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$v : speed of wave$ $v:"speed of wave"$
$f_{A} : The frequency of the sound heard by the observer A.$ $f_A:"The frequency of the sound heard by the observer A."$
$f_{B} : The frequency of the sound heard by the observer B.$ $f_B:"The frequency of the sound heard by the observer B."$
$v_{S} : speed of source$ $v_S:"speed of source"$
$f_{S} : source frequency$ $f_S:"source frequency"$

$frequency for the observer A:$ $"frequency for the observer A: "$

$f_{A} = f_{S} (\frac{v}{v + v_{S}})$ $f_A=f_S(v/(v+v_S))$

$frequency for the observer B:$ $"frequency for the observer B: "$

$f_{B} = f_{S} (\frac{v}{v - v_{S}})$ $f_B=f_S(v/(v-v_S))$

$f_{B} = f_{A} + 0.16 f_{A}$ $f_B=f_A+0.16 f_A$

$cancel(f_S)(v/(v-v_S))=cancel(f_S)(v/(v+v_S))+0.16(cancel(f_S)(v/(v+v_S)))$

$(v/(v-v_S))=(v/(v+v_S))+0.16(v/(v+v_S))$

$(cancel(v)/(v-v_S))=(cancel(v)/(v+v_S))(1+0.16)$

$1/(v-v_S)=(1.16)/(v+v_S)$

$1.16v-1.16v_S=v+v_S$

$1.16v-v=v_S+1.16v_S$

$0.16v=2.16v_S$

$v=340 m/s$

$0.16*340=2.16*v_S$

$v_S=(0.16*340)/(2.16)$

$v_S=25.19" "m/s$

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