Question

Two cars are moving on two perpendicular roads towards a crossing with uniform speeds of 72 km/h and 36 km/h. 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 car makes angle of 45 with the roads, will be

• A. 321 Hz
• B. 298 Hz
• C. 289 Hz
• D. 280 Hz

Answer 1

Answer: (B)

298 Hz

The component of velocity of source along line joining
$v_s=v_{1}cos{45}^o=36\times \frac{1}{\sqrt{2}}$
$=5\sqrt{2}m/s$
Component of velocity of observer along line joining
$v_0=v_{2}cos{45}^o$
$72\times \frac{1}{\sqrt{2}}$
$=10\sqrt{2}$
The frequency of horn
$n^{\prime }=\frac{v+v_0}{v-v_s}$
$n=\frac{330+10\sqrt{2}}{330-5\sqrt{2}}\times 280$
$=\frac{344}{323}\times 280=298Hz$