State the Doppler shift equation for a target moving with radial velocity v and wavelength λ.

State the Doppler shift equation for a target moving with radial velocity v and wavelength λ.

• A. f_d = v / λ
• B. f_d = 2 v / λ
• C. f_d = v f_0 / c
• D. f_d = 2 c / λ

Answer: (B)

In radar, the Doppler effect causes a frequency shift on the returned signal that is twice the one-way shift because the wave experiences the Doppler effect on both the outbound trip and the inbound echo. For a target moving with radial velocity v and a wavelength λ, the one-way Doppler shift is Δf = v/λ. Double that for the round trip, giving Δf = 2 v/λ. This can also be written using f0 = c/λ as Δf = 2 f0 v / c. So the correct relationship is f_d = 2 v / λ. The other forms miss the factor of two (they reduce to v/λ) or mix definitions.

In radar, the Doppler effect causes a frequency shift on the returned signal that is twice the one-way shift because the wave experiences the Doppler effect on both the outbound trip and the inbound echo. For a target moving with radial velocity v and a wavelength λ, the one-way Doppler shift is Δf = v/λ. Double that for the round trip, giving Δf = 2 v/λ. This can also be written using f0 = c/λ as Δf = 2 f0 v / c. So the correct relationship is f_d = 2 v / λ. The other forms miss the factor of two (they reduce to v/λ) or mix definitions.