What is the Doppler effect?

The change in observed frequency when source and observer move relative to each other. Toward each other: higher frequency. Apart: lower frequency.

What is the formula for sound?

f' = f₀ (v_w + v_obs)/(v_w + v_src). Sign convention: v_src is positive when the source moves away from the observer; v_obs is positive when the observer moves toward the source.

The shift to longer wavelengths (lower frequencies) of light from a receding source. Cosmological redshift z = Δλ/λ₀ ≈ v/c for v ≪ c.

When does the non-relativistic formula fail?

When v approaches c. For galaxies at high z, the full relativistic Doppler formula or general-relativistic expansion is needed.

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NSW · HSCModule 7

Doppler shift calculator

Classical Doppler for sound, non-relativistic approximation for light. Useful for redshift questions and the astrophysics applications in HSC Physics.

Inputs

Wave typeSource frequency f₀ (Hz)Wave speed v_w (m/s)Sound in air ≈ 340 m/sSource velocity (toward observer +) (m/s)Observer velocity (toward source +) (m/s)

Result

Observed frequency f'

415.6Hz

Shift Δf

-24.44Hz

f' = f₀ (v_w + v_obs) / (v_w + v_src). Sign convention: source velocity is positive away from observer; observer velocity is positive toward source.

How this calculator works

For sound, the calculator applies f' = f₀ (v_w + v_obs)/(v_w + v_src) using the conventional NESA sign choice. For light, the simple form Δλ/λ₀ = v/c is used, valid for low velocities (well below c).

Common questions

What is the Doppler effect?: The change in observed frequency when source and observer move relative to each other. Toward each other: higher frequency. Apart: lower frequency.
What is the formula for sound?: f' = f₀ (v_w + v_obs)/(v_w + v_src). Sign convention: v_src is positive when the source moves away from the observer; v_obs is positive when the observer moves toward the source.
What is redshift?: The shift to longer wavelengths (lower frequencies) of light from a receding source. Cosmological redshift z = Δλ/λ₀ ≈ v/c for v ≪ c.
When does the non-relativistic formula fail?: When v approaches c. For galaxies at high z, the full relativistic Doppler formula or general-relativistic expansion is needed.