The actual wavelength can be determined by comparing the two diametrically opposed listeners along the direction of the source's motion (in our case, #1 and #4). The apparent wavelength "heard" by listener #1 can be stated with the equation
λ_{1} = λ_{actual} + Δλ
while the apparent wavelength "heard" by listener #4 can be state with the equation
λ_{4} = λ_{actual} - Δλ
remembering that the Δ means the difference (in this case the apparent wavelength and the actual). Adding these two simultaneous equations yields the equation
λ_{1} + λ_{4 }= 2λ_{actual} |