Question 115: Waves

Question

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.

Accepted Answer

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

Waves

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.

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