Question

The speed limit for vehicles on a road is 100 Km/hr. A drop of 20% in the pitch of a car horn is detected by a policeman when the car passes him. Does the car driver crosses the speed limit. (Velocity of sound in air = 340 m/s)

Answer 1

Given that,

Speed limit $v_L=100km/hr$

Velocity of sound $v=340m/s$

By

We know that,

$n_A=\left(\frac{v}{v-v_S}\right)n.....\left(I\right)$

$n{{}^{\prime }}_A=\left(\frac{v}{v+v_S}\right)n.....\left(II\right)$

Now,

Divided equation (I) by (II)

$\frac{n_A}{n{{}^{\prime }}_A}=\frac{v+v_S}{v-v_S}$

$\frac{n_A}{n{{}^{\prime }}_A}=\frac{340+v_S}{340-v_S}$

$\frac{1}{0.8}=\frac{340+v_S}{340-v_S}$

$340-v_S=272+0.8v_S$

$68=1.8v_S$

$v_S=37.78m/s$

$v_S=136km/h$

Hence, this is the required solution