Doppler Effect for Sound: Simple Calculations and Signs

Concept: motion changes effective wavelength/arrival rate. Motion changes effective wavelength reaching the observer. With sound speed roughly fixed, changing spacing means you encounter wavefronts more or less often, shifting the observed frequency.

Concept: approaching compresses wavefronts. Wavefronts are compressed when approaching. That increases the encounter rate of wave crests, which is what frequency measures.

Concept: approach → f increases above emitted. Approaching → frequency increases, so a value above 500 Hz makes sense. The exact value depends on speed, but it must be higher than 500 Hz for approach.

Concept: receding → f decreases below emitted. Receding → observed frequency decreases below emitted. So a value like 440 Hz is consistent with moving away, while values above 500 Hz would indicate approaching.

As a source of waves approaches an observer, the waves in front of the source are compressed, leading to a decrease in wavelength. This phenomenon is known as the Doppler effect, where the frequency of the waves increases as the source moves closer, resulting in shorter wavelengths. Consequently, the closer the source gets, the more pronounced this effect becomes, causing the wavelength in front of the source to become shorter.

Concept: use λ = v/f. λ = v/f = 340/340 = 1.0 m. This relationship links speed, frequency, and wavelength in the same medium.

Concept: v = fλ with v constant. v = fλ; with v constant, λ = v/f. So increasing f forces λ to decrease, meaning wavefronts are closer together.

Concept: observer motion changes how often wavefronts are met. Observer motion toward source increases encounter rate of wavefronts. Even though the speaker emits the same frequency, the moving listener meets the crests more often.

Concept: moving away reduces encounter rate. Moving away decreases wavefront encounter rate. That lowers the observed frequency compared with standing still.

Concept: only radial motion changes spacing along the path. Only motion toward/away (radial component) changes spacing along the path. Sideways motion may change loudness with distance, but it gives little/no frequency shift in the basic model.

Concept: basic Doppler uses radial velocity. Basic Doppler uses radial motion; sideways motion gives little/no shift. At the instant of pure sideways motion, the distance isn't changing, so the frequency shift is minimal.

The concept relates to the Doppler effect, which describes how the frequency of waves changes based on the relative motion of the source and the observer. When a source of sound or light is moving towards an observer, the waves are compressed, leading to an increase in observed frequency. Conversely, when the source is moving away, the waves are stretched, resulting in a decrease in observed frequency. This phenomenon is crucial in various fields, including astronomy and radar technology, to determine the movement of stars and other objects.

Concept: lower observed frequency indicates separation increasing. 760 Hz is below 800 Hz → receding (or observer moving away). Loudness changes don't cause this shift; the key clue is the frequency decrease.

Concept: source frequency is set by the source; motion changes observation. The source emits at its own frequency; motion changes what is observed. Doppler shift is about wavefront spacing and encounter rate, not a 'retuned' siren.

Concept: Doppler is spacing/arrival-rate, not medium speed change. Doppler is about spacing/arrival rate. The sound speed is mostly set by the medium, but motion changes the effective wavelength reaching the observer.

Concept: λ scales inversely with f when v is constant. If f increases by 10%, λ = v/f decreases by about 1/1.1 ≈ 0.91 (≈ 9% shorter). This is why the change is not exactly 10%—it’s the inverse relationship.

Concept: shift depends on speeds and direction, not colour. a, b, d matter; colour is irrelevant. Faster motion and slower sound speed generally produce a larger fractional shift.

Concept: fractional shift scales roughly with speed ratio to v. Doppler shift scales with v_s/v or v_o/v; larger v reduces the fractional effect. With faster wave speed, the same motion causes a smaller proportional change in arrival rate.

Concept: speed can be inferred from a measured frequency shift. Speed can be inferred from frequency shift. Many instruments measure a shift and use known wave speed and geometry to calculate the target’s velocity.

Concept: motion changes what frequency you detect and thus wavelength in the medium. Motion changes what frequency you detect. If the medium speed is about constant, the observed frequency and wavelength shift together.