A policeman on duty detects a drop of 15 % in the pitch of the horn of a motor car as it crosses him. If the velocity of sound is 330 ~ms ⁻¹ , then calculate the speed of the car.

Step-by-step solution

Given, velocity of sound, v=330 ~m / s Let frequency of horn be f and speed of the car be v_ c . The frequency of the horn of the car heard by the policeman before it crosses him is given as f^ =f ( v v-v_ c ) ...(i) and after it crosses him is given as f^ =f ( v v+v_ c ) ...(ii) From Eqs. (i) and (ii), we get aligned f^ f^ &= v-v_ c v+v_ c = 330-v_ c 330+v_ c f^ f^ &= 330-v_ c 330+v_ c ...(iii) aligned Since, f^ =f^ -15 % of f^ =0.85 f^ From Eq. (iii), we get 0.85 f^ f^ = 330-v_ c 330+v_ c 0.85= 330-v_ c 330+v_ c