The driver of a bus approaching a big wall notices that the frequency of his bus’s horn changes from 420 Hz to 490 Hz ….

Q: The driver of a bus approaching a big wall notices that the frequency of his bus’s horn changes from 420 Hz to 490 Hz when he hears it after it gets reflected from the wall . Find the speed of bus if speed of the sound is 330 m/s

(a) 91 km/h

(b) 61 km/h

(c) 81 km/h

(d) 71 km/h

Click to See Solution :
Ans: (a)
Sol: Frequency appeared at wall

$\displaystyle f’ = \frac{v}{v-v_b}\times f $

$\displaystyle f’ = \frac{330}{330-v_b}\times f $ …(i)

Now Frequency of reflected sound ,

$\displaystyle f” = \frac{330 + v_b}{330}\times f’ $

$\displaystyle f” = \frac{330 + v_b}{330}\times \frac{330}{330-v_b}\times f $ from(i)

$\displaystyle f” = \frac{330 + v_b}{330-v_b}\times f $

$\displaystyle 490 = \frac{330 + v_b}{330-v_b}\times 420 $

vb = 25.4 m/s = 91 km/h