Doppler Effect
The Doppler effect is the apparent change in frequency (and thus pitch or colour) of a wave perceived by an observer when the source of the wave and the observer are moving relative to each other. When a source approaches, the observed frequency increases; when it recedes, the frequency decreases. The effect is named after Austrian physicist Christian Doppler (1842) and applies to all wave types including sound, light, and radar, with applications in medical ultrasound, police speed guns, weather radar, and astronomical redshift measurements.
Key Formula
f_obs = f_s × (v ± v_o) / (v ∓ v_s)
LaTeX: f_{obs} = f_s \left(\frac{v \pm v_o}{v \mp v_s}\right)
| Symbol | Meaning | Unit |
|---|---|---|
| f_{obs} | Observed frequency | Hz |
| f_s | Source frequency | Hz |
| v | Speed of sound in the medium | m/s |
| v_o | Speed of observer (+ toward source) | m/s |
| v_s | Speed of source (− toward observer) | m/s |
Worked Example
Problem
An ambulance siren emits sound at 700 Hz and travels toward a stationary observer at 30 m/s. The speed of sound is 340 m/s. What frequency does the observer hear?
Solution
Step 1: Identify values. f_s = 700 Hz, v = 340 m/s, v_s = 30 m/s (toward observer), v_o = 0. Step 2: Use f_obs = f_s × (v + v_o) / (v − v_s) (source approaching, observer stationary). Step 3: f_obs = 700 × (340 + 0) / (340 − 30) = 700 × 340 / 310. Step 4: f_obs = 700 × 1.0968 ≈ 767.7 Hz.
Answer
Observed frequency ≈ 767.7 Hz (higher pitch as source approaches)
Doppler Effect Scenarios for Sound (v_sound = 340 m/s)
| Scenario | Source Speed (m/s) | Observer Speed (m/s) | Formula Used | Effect on Frequency |
|---|---|---|---|---|
| Source approaching, observer still | 30 | 0 | f_s × v/(v − v_s) | Increases |
| Source receding, observer still | 30 | 0 | f_s × v/(v + v_s) | Decreases |
| Observer approaching, source still | 0 | 20 | f_s × (v + v_o)/v | Increases |
| Observer receding, source still | 0 | 20 | f_s × (v − v_o)/v | Decreases |
| Both approaching | 20 | 20 | f_s × (v + v_o)/(v − v_s) | Greatly increases |
Interactive Tools
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Related Terms
Sound Intensity
Sound intensity is the power carried by a sound wave per unit area perpendicular to the direction of propagation, measured in watts per square metre (W/m²). It quantifies how much acoustic energy passes through a given surface each second and decreases with the square of the distance from a point source — the inverse square law. Sound intensity is the physical basis for the decibel scale and is central to audiology, architectural acoustics, and occupational noise exposure standards.
Ultrasound
Ultrasound refers to sound waves with frequencies above the upper limit of human hearing, typically above 20,000 Hz (20 kHz), extending to several gigahertz in specialised applications. Because of its high frequency and corresponding short wavelength, ultrasound can resolve fine structural details and is strongly absorbed or reflected by tissue boundaries, making it invaluable in medical diagnostics (obstetric scans, echocardiography), industrial non-destructive testing, sonar navigation, and the sonication used in cleaning and chemical processing.
Wave Diffraction
Wave diffraction is the bending and spreading of waves around obstacles or through openings, occurring most prominently when the wavelength of the wave is comparable in size to the obstacle or aperture. The phenomenon is a direct consequence of Huygens's principle, which states that every point on a wavefront acts as a source of secondary wavelets. Diffraction is exploited in X-ray crystallography to determine molecular structures, in radio communication to allow signals to travel around hills, and in optical instruments to understand resolution limits.
Named after Austrian mathematician and physicist Christian Andreas Doppler (1803–1853), who first described the effect in his 1842 paper "Über das farbige Licht der Doppelsterne" (On the Coloured Light of the Binary Stars).