Question

Two cars are moving on two perpendicuiar 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 $45^{\circ }$ with the roads, will be

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

Answer 1

Answer: (B)

The component of velocity of source along line joining
$v_s=v_{1}cos45^{\circ }$
$=36\times \frac{1}{\sqrt{2}}km/h$
$=5\sqrt{2}m/s$
Component of velocity of observer (second car) along line joining
$v_0=v_{2}cos45^{\circ }=72\times \frac{1}{\sqrt{2}}km/h=10\sqrt{2}m/s$
$n^{\prime }=\frac{v+v_0}{v-v_s}n=\frac{330+10\sqrt{2}}{300-5\sqrt{2}}\times 280$
$=\frac{344}{323}\times 280Hz=298Hz$