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14. waves and sound — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics14. waves and sound1 Mark
MCQ
A driver in a car, approaching a vertical wall notices that the frequency of his car horn, has changed from $440\, Hz$ to $480 \,Hz ,$ when it gets reflected from the wall. If the speed of sound in air is $345 \,m / s ,$ then the speed of the car is $.......km/hr$
  • A
    $36$
  • B
    $24$
  • C
    $18$
  • ✓
    $54$
✓

Answer

Correct option: D.
$54$
d
$f _{1}=$ frequency heard by wall $= f _{ s }=\left(\frac{ v _{ s }}{ v _{ s }- v _{ c }}\right)$

$f _{2}=$ frequency heard by driver after reflection from wall

$f_{2}=\left(\frac{v_{s}+v_{c}}{v_{s}}\right) f_{1}=\left(\frac{v_{s}+v_{c}}{v_{s}-v_{c}}\right) f_{0}$

$\frac{f_{2}}{f_{0}}=\frac{v_{s}-v_{c}}{v_{s}+v_{c}}$

$\frac{48}{44}=\frac{v_{s}-v_{c}}{v_{s}+v_{c}}$

$12\left( v _{ s }+ v _{ c }\right)=11\left( v _{ s }- v _{ c }\right)$

$23 v _{ c }= v _{ s }$

$v _{ c }=\frac{ v _{ s }}{23}=\frac{345}{23}=15 m / s$

$=\frac{15 \times 18}{5}=54 km / hr$

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