The Doppler effect experiment investigates the change in the observed frequency of sound when there is relative motion between a sound source and an observer.
When a sound source approaches an observer, the spacing between wavefronts becomes smaller, so the observed frequency becomes higher than the source frequency. Conversely, when the source moves away from the observer, the wavefront spacing becomes larger and the observed frequency becomes lower.
In an experimental report, it is important not only to record the frequencies during approach and recession, but also to discuss how source speed, speed of sound, direction of motion, distance from the microphone, frequency analysis, reflected sound, and other factors affect the results.
This article assumes an experiment in which a speaker emitting a constant-frequency sound is mounted on a cart and moved toward and away from a fixed microphone. It summarizes the items to record, sample experimental values, calculations, sources of error, example results, and discussion examples.
Note:
This article is a study reference for discussing results obtained in physics experiments at universities and similar institutions. The experimental values shown are illustrative examples and are not actual measurement results.
For the use and safety precautions of carts, speakers, oscillators, microphones, rails, speed sensors, and other equipment, always follow your university laboratory manual and the instructions of your instructor or TA. Do not suddenly stop a moving cart by hand or place objects in its path.
- What Is the Doppler Effect?
- Main Items to Record in the Results
- Sample Experimental Conditions
- Sample Experimental Values
- Calculation Methods
- Calculating the Speed of Sound from Room Temperature
- Theoretical Frequency During Approach
- Theoretical Frequency During Recession
- Average Observed Frequency
- Relative Error
- Calculating Source Speed from Observed Frequency
- Calculating Speed from Both Approach and Recession Frequencies
- Velocity Component for an Oblique Pass
- Main Sources of Error
- Example of Writing the Results
- Points to Connect to the Discussion
- Discussion Example
- Summary
What Is the Doppler Effect?
When a sound source is stationary, sound waves emitted by the source spread through the surrounding air at the speed of sound v. If the source frequency is f0, the wavelength produced by a stationary source is:
λ = v / f0
When the source approaches the observer at speed vs, it moves toward the observer during each period, so the wavelength in front of the source becomes shorter.
λapproach = (v − vs) / f0
Therefore, the frequency received by a stationary observer during approach is:
fapproach = f0 × v / (v − vs)
When the source moves away from the observer, the wavelength behind it becomes longer, so the observed frequency is:
frecede = f0 × v / (v + vs)
Here we consider the case in which the observer and air are stationary and only the source moves along a straight line.
When the Observer Moves
If the source is stationary and the observer approaches it at speed vo, the observer encounters more wavefronts per unit time, so the observed frequency is:
f = f0 × (v + vo) / v
Note that the form of the equation differs depending on whether the source or the observer is moving.
Main Items to Record in the Results
- Nominal source frequency
- Reference frequency measured while stationary
- Room temperature
- Speed of sound calculated from room temperature
- Speed of the cart carrying the source
- Direction of cart motion
- Observed frequency during approach
- Observed frequency during recession
- Theoretical approach frequency
- Theoretical recession frequency
- Difference between observed and theoretical values
- Relative error
- Frequency shift
- Average of repeated measurements
- Minimum distance between microphone and source
- Angle between the source direction of motion and the line to the microphone
- Peak position in the frequency spectrum
- Presence of reflected sound or background noise
The Doppler effect depends on the component of source velocity along the line joining the source and observer. If the source does not pass directly in front of the microphone, use the line-of-sight velocity component rather than the full cart speed.
Sample Experimental Conditions
| Item | Sample Condition |
|---|---|
| Sound source | Small speaker connected to an oscillator |
| Source frequency f0 | 1000 Hz |
| Cart speed vs | 5.00 m/s |
| Observer | Fixed microphone |
| Room temperature | 20.0 ℃ |
| Speed of sound v | 343.5 m/s |
| Measurement method | Frequency analysis of recorded waveform |
| Number of measurements | Three each during approach and recession |
Sample Experimental Values
Measurements During Approach and Recession
| Trial | Observed Frequency During Approach (Hz) | Observed Frequency During Recession (Hz) |
|---|---|---|
| 1 | 1015 | 986 |
| 2 | 1014 | 985 |
| 3 | 1016 | 986 |
Average and Theoretical Values
| Condition | Experimental Average (Hz) | Theoretical Value (Hz) | Relative Error (%) |
|---|---|---|---|
| Approach | 1015 | 1014.8 | 0.02 |
| Recession | 985.7 | 985.6 | 0.01 |
In these sample values, the observed frequency is higher than 1000 Hz as the source approaches the microphone and lower as it moves away.
Sample Values for Different Source Speeds
| Source Speed (m/s) | Approach Frequency (Hz) | Recession Frequency (Hz) | Difference (Hz) |
|---|---|---|---|
| 2.00 | 1006 | 994 | 12 |
| 3.00 | 1009 | 991 | 18 |
| 4.00 | 1012 | 988 | 24 |
| 5.00 | 1015 | 986 | 29 |
| 6.00 | 1018 | 983 | 35 |
As source speed increases, the approach frequency increases and the recession frequency decreases.
Calculation Methods
Calculating the Speed of Sound from Room Temperature
At a room temperature of 20.0 ℃, the speed of sound in air can be estimated using:
v = 331.5 + 0.60t
= 331.5 + 0.60 × 20.0
= 343.5 m/s
Theoretical Frequency During Approach
For a source frequency of 1000 Hz, sound speed of 343.5 m/s, and source speed of 5.00 m/s:
fapproach = f0 × v / (v − vs)
= 1000 × 343.5 / (343.5 − 5.00)
= 343500 / 338.5
= 1014.8 Hz
Theoretical Frequency During Recession
frecede = f0 × v / (v + vs)
= 1000 × 343.5 / (343.5 + 5.00)
= 343500 / 348.5
= 985.6 Hz
Average Observed Frequency
If the three approach measurements are 1015, 1014, and 1016 Hz:
Average frequency = (1015 + 1014 + 1016) / 3
= 1015 Hz
Relative Error
For an experimental approach value of 1015 Hz and theoretical value of 1014.8 Hz:
Relative error (%) = |Experimental value − Theoretical value| / Theoretical value × 100
= |1015 − 1014.8| / 1014.8 × 100
= approximately 0.02%
Calculating Source Speed from Observed Frequency
Solving the approach equation for source speed gives:
vs = v(1 − f0/fapproach)
Using an observed frequency of 1015 Hz:
vs = 343.5 × (1 − 1000/1015)
= 343.5 × 0.01478
= 5.08 m/s
Calculating Speed from Both Approach and Recession Frequencies
Using both observed frequencies can reduce the influence of an offset in the reference frequency.
vs = v × (fapproach − frecede) / (fapproach + frecede)
For 1015 Hz during approach and 985.7 Hz during recession:
vs = 343.5 × (1015 − 985.7) / (1015 + 985.7)
= 343.5 × 29.3 / 2000.7
= 5.03 m/s
Velocity Component for an Oblique Pass
If the angle between the source direction of motion and the direction from the source to the microphone is θ, the velocity component contributing to the Doppler effect is:
vradial = vs cos θ
At the instant the source passes directly beside the microphone, θ = 90°, so the line-of-sight velocity is zero and the observed frequency ideally approaches the original frequency.
Main Sources of Error
| Source of Error | Effect on Measurement | Likely Trend in Results | Improvement / Check |
|---|---|---|---|
| Cart speed is not constant | Doppler shift changes during measurement | Frequency peak broadens | Analyze only the constant-speed interval |
| Source does not pass directly in front of microphone | Line-of-sight velocity component is reduced | Frequency shift is smaller than theory | Align rail and microphone on the same straight line |
| Oscillator frequency error | Reference frequency differs from setting | Both approach and recession values shift | Use the measured stationary frequency as reference |
| Insufficient temperature correction of sound speed | Theoretical frequency is incorrect | Systematic difference from experiment | Measure room temperature at the experiment location |
| Reflections from walls or floor | Direct and reflected sounds overlap | Multiple peaks appear in the spectrum | Measure in a low-reflection environment |
| Background noise | Makes target frequency peak difficult to identify | Greater frequency variation | Record in a quiet environment |
| Analysis window too long | Averages changes from approach to recession | Peak broadens and shift appears smaller | Use a shorter time window |
| Analysis window too short | Insufficient frequency resolution | Peak frequency cannot be determined precisely | Balance velocity variation and frequency resolution |
| Microphone directivity | Receiving sensitivity varies with source position | Amplitudes differ between approach and recession | Point microphone toward the travel path |
| Wind or airflow | Changes sound propagation relative to the ground | Small deviation from theory | Measure indoors with little airflow |
Why the Frequency Increases During Approach
While the source emits one wave per period, it also moves toward the observer. Therefore, the spacing between successive wavefronts emitted toward the observer is shorter than when the source is stationary.
Because the speed of sound is nearly constant, a shorter wavelength means more wavefronts reach the observer per unit time, producing a higher observed frequency.
Why the Frequency Decreases During Recession
When the source moves away from the observer, it moves farther away before emitting the next wave. Thus, the spacing between wavefronts reaching the observer is greater than in the stationary case.
With constant sound speed, a longer wavelength means fewer wavefronts arrive per unit time, so the observed frequency is lower.
Why the Frequency Changes Rapidly Near the Closest Point
While the source approaches the microphone, its line-of-sight velocity is directed toward the microphone, so the observed frequency is high. At the instant it passes directly beside the microphone, the line-of-sight velocity approaches zero, and immediately afterward it changes to the receding direction.
Thus, the observed frequency changes from the higher approach value to the lower recession value. However, if the source passes at some distance from the microphone, the change is continuous and does not necessarily switch instantaneously.
Why the Observed Frequency Peak Broadens
Even when the cart moves at constant speed, the direction joining the source and microphone changes with time. Consequently, the line-of-sight velocity also changes, and the observed frequency varies slightly even during a short recording.
If this signal is analyzed over a long time interval, multiple frequencies are averaged and the peak broadens. Time-frequency analysis such as the short-time Fourier transform is useful for observing frequency changes over time.
Example of Writing the Results
A speaker emitting a 1000 Hz tone was mounted on a cart and moved toward a fixed microphone at 5.00 m/s, then moved away at the same speed. The room temperature was 20.0 ℃, and the speed of sound was taken as 343.5 m/s.
The observed frequency during approach was 1014–1016 Hz, with an average of 1015 Hz. During recession it was 985–986 Hz, with an average of 985.7 Hz.
The theoretical values were 1014.8 Hz during approach and 985.6 Hz during recession, in good agreement with the experimental values. The Doppler effect, in which the frequency increases as the source approaches the observer and decreases as it moves away, was confirmed.
Points to Connect to the Discussion
- How did the observed frequency change between approach and recession?
- Did the experimental values agree with the Doppler-effect equations?
- Did a greater source speed produce a greater frequency shift?
- Was the measured stationary frequency used as the reference?
- Was the speed of sound calculated from room temperature used?
- Did the source approach the microphone along a straight line?
- Was the cart speed constant over the measurement interval?
- Did reflected sound or background noise affect the spectrum?
- Was the frequency-analysis time window appropriate?
- Did the changing line-of-sight velocity near the closest point affect the result?
- Did the source speed calculated from approach and recession frequencies agree with the measured speed?
Discussion Example
In this experiment, a speaker emitting a constant-frequency sound was mounted on a cart, and the observed frequencies were measured as it approached and moved away from a fixed microphone.
The stationary source frequency was 1000 Hz. When the cart moved at 5.00 m/s, the average observed frequency was 1015 Hz during approach and 985.7 Hz during recession. Because the frequency increased as the source approached the microphone and decreased as it moved away, the Doppler effect was confirmed.
Using a sound speed of 343.5 m/s at a room temperature of 20.0 ℃, the theoretical frequencies were 1014.8 Hz during approach and 985.6 Hz during recession. The relative errors were small in both cases, indicating good agreement between the measurements and theory.
The frequency increased during approach because the source moved toward the microphone while emitting successive waves, reducing the spacing between wavefronts in front of it. Since the sound speed is constant, a shorter wavelength causes more wavefronts to reach the microphone per unit time, increasing the observed frequency.
Conversely, when the source moved away, the spacing between successive wavefronts increased. Therefore, fewer wavefronts reached the microphone per unit time, and the observed frequency became lower than the stationary value.
Increasing the source speed also increased the difference between the observed frequencies during approach and recession. This is because the source travels farther during each period, producing a larger change in the wavelengths in front of and behind it.
Possible causes of differences between experimental and theoretical values include variations in cart speed, misalignment between the source path and microphone, oscillator frequency error, temperature correction of sound speed, reflections from walls and floor, and the time window used for frequency analysis.
In particular, only the component of source velocity along the line joining the source and microphone directly contributes to the Doppler effect. If the source does not approach the microphone along a straight line, this component is smaller than the cart speed, and the observed frequency shift is also smaller than the theoretical value calculated using the full speed.
Furthermore, as the source passes near the microphone, the direction joining the source and microphone changes continuously, so the line-of-sight velocity also changes. If a long time interval is analyzed at once, different frequency components may be averaged and the spectral peak may broaden.
To improve measurement accuracy, only the interval in which the cart moves at constant speed should be analyzed, and the source and microphone should be aligned along the same straight line. It is also effective to measure the stationary source frequency directly, use short analysis windows, and conduct the experiment in an environment with little reflected sound.
These results confirm that relative motion between a sound source and an observer changes the observed frequency: it becomes higher during approach and lower during recession. They also show that the source speed can be determined from the observed frequency shift.
Discussion Example When the Frequency Shift Is Smaller Than Theory
If the observed frequency shift was smaller than the theoretical value, one possible reason is that the source did not approach the microphone along a straight line, so only the line-of-sight component of the cart velocity contributed to the Doppler effect. Another possible factor is that a long analysis interval included both approach and recession, averaging different frequencies.
Discussion Example When Multiple Peaks Appear in the Frequency Spectrum
If multiple peaks appeared in the frequency spectrum, reflected sound from walls or the floor may have reached the microphone along paths different from the direct sound. Multiple peaks may also occur if the speaker contains harmonics in addition to the fundamental frequency or if noise from the moving cart overlaps the signal.
Summary
In a Doppler effect experiment, relative motion is created between a sound source and an observer, and the observed frequencies during approach and recession are measured.
As the source approaches the observer, the wavelength becomes shorter and the observed frequency increases. As it moves away, the wavelength becomes longer and the observed frequency decreases.
In the discussion, it is important to relate source speed, line-of-sight velocity, speed of sound, room temperature, direction of motion, frequency analysis, reflected sound, background noise, and other factors to the results.
