The frequency of a car horn encountered a change from 400 Hz to 500 Hz, when the car approaches a vertical wall. If the speed of sound is 330 m/s. Then the speed of car is ___________ km/h.

$\because$ Since, frequency received by the wall,<br/><br/>$f' = \left( {{{{v_s}} \over {{v_s} - v}}} \right){f_o}$ .... (i)<br/><br/>where, v_s = velocity of sound in air, v = velocity of car and f_o = observed frequency of sound.<br/><br/>Reflected frequency received by man is<br/><br/>$f'' = \left( {{{{v_s} + v} \over {{v_s}}}} \right)f'$ ..... (ii)<br/><br/>From Eqs. (i) and (ii), we get<br/><br/>$$f'' = \left( {{{{v_s} + v} \over {{v_s}}}} \right)\left( {{{{v_s}} \over {{v_s} - v}}} \right){f_o} \Rightarrow f'' = \left( {{{{v_s} + v} \over {{v_s} - v}}} \right){f_o}$$<br/><br/>$$ \Rightarrow 500 = \left( {{{330 + v} \over {330 - v}}} \right) \times 400 \Rightarrow {{500} \over {400}} = {{(330 + v)} \over {(330 - v)}}$$<br/><br/>$\Rightarrow 5(330 - v) = 4(330 + v) \Rightarrow 1650 - 5v = 1320 + 4v$<br/><br/>$\Rightarrow 9v = 330 \Rightarrow v = {{330} \over 9}$ m/s<br/><br/>or $v = {{330} \over 9} \times {{18} \over 5} = 132$ km/h