MCAT content library / Chemistry & physics / Doppler shifts and ultrasound
Use relative motion to predict the direction and size of a frequency shift, then recognize why a reflected wave can undergo two Doppler shifts.
About 16 minutes, including the moving-reflector example and checks.
Useful foundations
On this page
- Approach raises observed frequency
- Concept: source motion and observer motion enter differently
- Worked application: reflection from a moving target
- Pattern: reflection can double the small-velocity shift
- Rule: Doppler shift does not change wave speed in the medium
- Check your reasoning
- Continue learning
- Sources
Approach raises observed frequency
The Doppler effect is a frequency change caused by relative motion between a wave source and an observer. For sound in a stationary medium, motion that brings source and observer closer together raises the observed frequency; motion that separates them lowers it.
The direction can often be solved qualitatively before using an equation. If wavefronts arrive more frequently because the separation is shrinking, observed frequency increases. If arrival intervals become longer because the separation grows, observed frequency decreases.
Concept: source motion and observer motion enter differently
For sound speed v in a stationary medium, a common one-dimensional form is:
f′ = f (v ± vo)/(v ∓ vs)
where vo is observer speed and vs is source speed. Choose signs so motion toward the other party raises the observed frequency and motion away lowers it.
Source motion changes the spacing of wavefronts in the medium. Observer motion changes the rate at which an observer encounters already-propagating wavefronts. Both can produce a Doppler shift, but they enter the equation in different places.
Worked application: reflection from a moving target
An original ultrasound-style experiment sends a 5.0 MHz sound wave toward a small reflector moving directly toward a stationary transducer at 0.50 m/s. The passage supplies a sound speed of 1540 m/s and, for speeds much smaller than the sound speed, the reflected-wave approximation:
Δf ≈ 2fu/v
where u is reflector speed along the beam direction.
Substitution gives:
Δf ≈ 2(5.0 × 10⁶ Hz)(0.50 m/s)/(1540 m/s) ≈ 3.25 × 10³ Hz.
Because the reflector approaches the transducer, the reflected frequency is higher than the transmitted frequency by about 3.25 kHz under the supplied approximation.
| Reflector motion | Sign of reflected shift |
|---|---|
| Toward transducer | Positive: returned frequency increases |
| Away from transducer | Negative: returned frequency decreases |
| Perpendicular to beam | Zero ideal axial shift in the simplified model |
Pattern: reflection can double the small-velocity shift
A moving reflector participates twice. First, it acts as a moving observer receiving the incident wave. Then the reflected wave returns as though emitted by a source moving with the reflector. For small target speeds compared with wave speed, those two shifts combine to produce the approximate factor of 2 in the supplied relation.
The geometry matters. Doppler measurements respond to the velocity component along the wave-propagation direction. A target moving entirely perpendicular to the beam has no first-order axial Doppler shift in the simplified one-dimensional model even though its actual speed is nonzero.
Rule: Doppler shift does not change wave speed in the medium
A changed observed frequency does not imply that sound travels faster through the same unchanged medium. The medium sets the propagation speed. Since v = fλ, a source-motion Doppler shift changes the wavelength pattern in the medium while the wave speed remains governed by the medium.
The ordinary subsonic source formula also has limits. When a source approaches or exceeds the wave speed, wavefronts can pile up into a shock front and the simple low-speed interpretation is no longer adequate. A passage should supply the relevant shock-wave or Mach-number relation if quantitative analysis is required.
ACTIVE PRACTICE · WAVE PHYSICS
Predict the Reflected Doppler Shift
The lesson’s stationary transducer emits 5.0 MHz ultrasound into a medium where sound speed is 1540 m/s. A reflector moves directly toward it at 0.50 m/s. Use the stated low-speed, axial reflection approximation Δf ≈ 2fu/v.
Axial speed toward transducer: m/s. Approximate signed shift: kHz. Returned frequency ≈ MHz.
Angle and velocity are teaching controls. Positive axial speed denotes approach, negative denotes recession. Perpendicular motion produces zero first-order axial shift. Sound speed is unchanged by this Doppler effect in the stated medium.
Check your reasoning
Choose an answer before opening its feedback.
Check 1
A sound source moves toward a stationary observer. What happens to the observed frequency?
A. It increases.
Correct. Approaching source motion compresses the arriving wavefront spacing.
B. It decreases.
Review this choice. A decrease corresponds to recession.
C. It must become zero.
Review this choice. The source still produces oscillations.
D. It changes only if sound speed changes.
Review this choice. Relative motion alone produces the Doppler effect.
Check 2
A reflector moves perpendicular to the beam in the simplified axial Doppler model. What is the first-order Doppler shift associated with that motion component?
A. Approximately zero
Correct. The axial velocity component is zero.
B. Maximum positive shift
Review this choice. Maximum axial shift occurs when motion is along the beam.
C. Maximum negative shift
Review this choice. Perpendicular motion is neither direct approach nor recession.
D. Infinite shift
Review this choice. The model predicts no axial shift for a zero axial component.
Check 3
The observed sound frequency changes while the medium and its temperature remain unchanged. What happens to the wave speed in that medium?
A. It remains approximately the same.
Correct. The medium governs sound speed; frequency and wavelength adjust consistently.
B. It must increase in direct proportion to frequency.
Review this choice. The wavelength changes so that v remains set by the medium.
C. It must decrease to zero.
Review this choice. A Doppler shift does not stop wave propagation.
D. It becomes the reflector speed.
Review this choice. Target speed and wave speed are different quantities.
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