The driver of 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 the bus if speed of the sound is 330 ms⁻¹ :

$f\text{'}=f\lfloor \frac{v+\frac{v}{4}}{v}\rfloor =\frac{5f}{4}$

$\Rightarrow \frac{f\text{'}}{f}=\frac{5}{4}$

$\Rightarrow \frac{\Delta f}{f}=\frac{1}{4}$

f? = frequency heard by wall = f_s (v_s/ (v_s - v_c)
f? = frequency heard by driver after reflection from wall

f? = (v_s + v_c)/v_s)f? = (v_s + v_c)/ (v_s - v_c)f?
f? /f? = (v_s - v_c)/ (v_s + v_c)
48/44 = (v_s - v_c)/ (v_s + v_c)
12 (v_s + v_c) = 11 (v_s - v_c)
23v_c = v_s
v_c = v_s/23 = 345/23 = 15 m/s
= (15 × 18)/5 = 54 km/hr

  $f_1=f_o\left(\frac{v}{v-v_s}\right)\mathrm{}{f}_1-f_2=2$

$f_2=f_o\left(\frac{v}{v+v_s}\right)\mathrm{}{f}_{0}v\left[\frac{v+v_s-\left(v-v_s\right)}{v^2-v_s^2}\right]=2;\mathrm{}\frac{2f_{0}v{v}_s}{v^2-v_s^2}=2$

$?{\mathrm{v}}_{\mathrm{s}}?\mathrm{v}\mathrm{}\therefore {\mathrm{v}}_{\mathrm{s}}=\frac{1}{4}\mathrm{m}/\mathrm{s}$