question_answer

Two cars are moving on two perpendicularroads towards a crossing with uniformspeeds of 72 km/h and 36 km/h. If first carblows horn of frequency 280 Hz, then thefrequency of horn heard by the driver ofsecond car when line joining the car makesangle of 45° with the roads, will be

A)  321 Hz                                 

B)  298 Hz

C)  289 Hz                                 

D)  280 Hz

Correct Answer: B

Solution :

                The component of velocity of source along line joining \[{{v}_{s}}={{v}_{1}}\,\cos {{45}^{o}}=36\times \frac{1}{\sqrt{2}}km/h=5\sqrt{2}m/s\] Component of velocity of observer (second car) along line joining                 \[{{v}_{0}}={{v}_{2}}\,\cos {{45}^{o}}=72\times \frac{1}{\sqrt{2}}km/h\]                 \[=10\sqrt{2}m/s\]                 \[n=\frac{v+{{v}_{0}}}{v-{{v}_{s}}}n=\frac{330+10\sqrt{2}}{330-5\sqrt{2}}\times 280\]                 \[=\frac{344}{323}\times 280Hz=298Hz\]