Discussion Forum

Two men are walking along a horizontal straight line in the same direction.The man in front walks at speed 1.0 ms^-1 and the man behind  walks at a speed 2.0 ms^-1 . A third man is standing at a height 12 m above the same horizontal line such that all three men are in a vertical plane. The two walking men are blowing identical whistles which  emit a sound of frequency 1430Hz. The speed of sound in air 330 ms^-1. At the instant , when the moving men are 10 m apart, the stationary man is equidistant from them. The frequency of beats in Hz, heard by the stationary man at this instant, is....

Answer:

Explanation:

   $f_{A}= 1430 [\frac{330}{330-2\cos\theta}]$

   $= 1430 [\frac{1}{1-\frac{2\cos\theta}{330}}]\approx 1430[1+\frac{2\cos \theta}{330}]$

                                                          [ from binomial expansion]

                $f_{B}=1430[\frac{330}{330+1\cos\theta}]$

                       $\approx1430[1-\frac{\cos \theta}{330}]$

     Beat frequency = $f_{A-}-f_{B}$

                         $=1430[\frac{3\cos \theta}{330}] =13\cos\theta$

                          $=13[\frac{5}{13}] =5.00 Hz$