In classical physics, where the speeds of source and the receiver relative to the medium are lower than the velocity of waves in the medium, the relationship between observed frequency #f # and emitted frequency #f_0# is given by Doppler's effect as
#f=((c+v_r)/(c+v_s))f_0#
where
#c->"the velocity of waves in the medium"#
#v_ r-> "the velocity of the receiver relative to the medium"# (positive if the receiver is moving towards the source (and negative in the other direction)
#v_s ->"the velocity of the source relative to the medium"#
(positive if the source is moving away from the receiver (and negative in the other direction )
In our problem
#c=343.2ms^-1#
#v_r=-v_r#
#v_s=+v_r#
#f_0=440Hz#
#f=438Hz#
So
#f=((c+v_r)/(c+v_s))f_0#
#=>438=((343.2-v_r)/(343.2+v_r))xx440#
#878v_r=(440-438)xx343.2#
#=>v_r=686.4/878~~0.782" m/s"#
