question_answer

Two cars are moving on two perpendicular roads towards a crossing with uniform speeds of 72 km/hr and 36 km/hr. If first car blows horn of frequency 280 Hz, then the frequency of horn heard by the driver of second car when line joining the cars make 45° angle with the roads; will be [RPET 1997]

A)            321 Hz                                     

B)            298 Hz  

C)            289 Hz                                     

D)            280 Hz

Correct Answer: B

Solution :

            Here \[{{v}_{A}}=72\,km/hr=20m/\sec \]                    \[{{v}_{B}}=36km/hr=10m/\sec \]                    \[n'=n\left( \frac{v+{{v}_{B}}\cos {{45}^{o}}}{v-{{v}_{A}}\cos {{45}^{o}}} \right)\]                                \[\Rightarrow \] \[n'=280\,\left( \frac{340+10/\sqrt{2}}{340-20/\sqrt{2}} \right)=298\,Hz\]