Question 159: Waves

Question

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 :

Accepted Answer

f
1
= frequency heard by wall
= $$\left( {{{{v_s} - 0} \over {{v_s} - {v_c}}}} ight){f_0}$$ = $${{{{v_s}} \over {{v_s} - {v_c}}} 	imes 440}$$
f
2
= frequency heard by driver after reflection from wall
= $$\left( {{{{v_s} + {v_c}} \over {{v_s} - 0}}} ight){f_1}$$
$$ \Rightarrow $$ 480 = $$\left( {{{{v_s} + {v_c}} \over {{v_s}}}} ight){f_1}$$
$$ \Rightarrow $$ 480 = $$\left( {{{{v_s} + {v_c}} \over {{v_s}}}} ight)\left( {{{{v_s}} \over {{v_s} - {v_c}}}} ight) 	imes 440$$
$$ \Rightarrow $$ 480 = $$\left( {{{{v_s} + {v_c}} \over {{v_s} - {v_c}}}} ight) 	imes 440$$
$$ \Rightarrow $$ 480 = $$\left( {{{345 + {v_c}} \over {345 - {v_c}}}} ight) 	imes 440$$
$$ \Rightarrow $$ 12 = $$\left( {{{345 + {v_c}} \over {345 - {v_c}}}} ight) 	imes 11$$
$$ \Rightarrow $$ 11 ÃÂ 345 + 11v
c
= 12 ÃÂ 345 Ã¢ÂÂ 12v
c
$$ \Rightarrow $$ v
c
= $${{345} \over {23}}$$ m/s = $${{345} \over {23}} 	imes {{18} \over 5}$$ = 54 km/hr

Answer

36 km/hr

Answer

54 km/hr

Answer

24 km/hr

Answer

18 km/hr

Waves

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 :

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