Question

Two cars are moving on two perpendicular roads towards a crossing with uniform speeds of 72 km/h and 36 km/h. If second car blows horn of frequency 280 Hz, then the frequency of horn heard by the driver of first car when the line joining the cars makes angle of ${45}^{\circ }$ with the roads, will be (velocity of sound is 330 m/s)

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

Answer 1

The correct option is B 298 Hz

The component of velocity of source along line joining the car is
$v_s=v_{1}cos{45}^{\circ }=36\times \frac{1}{\sqrt{2}}km/h$
$=5\sqrt{2}m/s$
Component of velocity of observer(second car) along the line joining the car is

$V_0=v_{2}cos{45}^{\circ }=72\times \frac{1}{\sqrt{2}}km/h$
$=10\sqrt{2}m/s$
$n^{\prime }=\frac{v+v_0}{v-v_s}n=\frac{330+10\sqrt{2}}{330-5\sqrt{2}}\times 280$
$=\frac{344}{323}\times 280Hz=298Hz$