A source of sound moves toward you at speed and away from Ma

A source of sound moves toward you at speed and away from Malcolm, who is standing on the other side of it. You hear the sound at twice the frequency as Malcolm. What is the speed of the source? Assume the speed of sound is 397.41m/s.

Solution

Speed of source v = ?

Speed of sound V = 397.41 m/s

Actual frequency f = f

Apperent frequency of you f \' = [V/(V-v)]f

Apperent frequency of Malcolm f \" = [V/(V+v)] f

According to problem, f \' = 2 f \"

                 [V/(V-v)]f = 2 [V/(V+v)]f

                  1/(V-v) = 2/(V+v)

                   V + v = 2( V-v)

                           =2V -2v

                   v+2v = 2V -V

                       3v = V

                         v = V / 3

                           = 397.41 / 3

                           = 132.47 m/s