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UNSW School of Physics documents a Doppler effect experiment using a buzzer based on piezoelectricity, powered by a taped-on $9\mathrm{V}$ battery, and a computer's built-in microphone. Audacity records the acoustic wave. First record the stationary source to establish its baseline frequency; then attach it to a bicycle passing the stationary microphone. The published spectrogram shows a rapid decrease in frequency during passage.^[ref]

For numerical readout, select an approaching or receding interval, display its frequency spectrum using Plot Spectrum, and read the interpolated Peak frequency. The protocol recommends repeating with slightly different selections to test stability, and working outdoors to reduce reflections and standing waves. Longer windows refine frequency spacing while averaging over more motion. The baseline controls for the source's actual tone; repeated selections expose analysis-window sensitivity.^[ref]

Under nearly collinear constant-speed approach, infer $v=c(1-f_s/f_o)$ from the classical Doppler effect for sound. For recession the positive speed is $v=c(f_s/f_o-1)$. These inversions need a specified speed of sound. An offset path changes the projection, as in Doppler frequency along a trajectory; neither inversion measures the full speed near closest passage. The protocol's controls cannot remove arbitrary acceleration, background measurement noise or unresolved reflected paths. No new measurements are claimed here.

Acoustic phonetics studies speech as a physical sound wave. A microphone records a signal related to changing sound pressure; analysis asks how its amplitude, timing and frequency content vary. A waveform displays variation over time, whereas a spectrogram displays the distribution of signal energy across both time and frequency.

For an original comparison, record a sustained vowel followed by a sustained hiss. Inspect each waveform at the same time scale and compare their spectrograms. Approximately repeated vocal cycles can give a harmonic structure, while the hiss provides an example of a noisier excitation. Broad spectral concentrations associated with the vocal tract are formants; they should be distinguished from the fundamental frequency of a repeating source. The spectrogram's analysis-window duration affects which temporal and spectral details are visible.^[ref]

These are measurements of the signal, rather than direct readings of a listener's perceived pitch or a speaker's tongue position. Relating the signal to perception and production requires auditory phonetics and articulatory phonetics.

A fricative is a consonant produced with a narrow constriction that generates sustained turbulent airflow and its associated noise. The articulators approach closely without creating the complete oral closure of a plosive. Place of articulation and voicing further distinguish different fricatives.^[ref]

Sustain [f] and then [v]. Both use the lower lip and upper teeth, but the second normally adds vocal fold vibration. A spectrogram can display a noise component and, where present, periodic structure. The physical source of the noise is the constricted airflow, while the vocal tract shapes its spectrum. Merely calling a sound unvoiced does not identify it as a fricative.

Frequency-resolved optical gating characterizes an ultrashort pulse using a nonlinear gate and a measured two-dimensional spectrogram. In second-harmonic frequency-resolved optical gating, split the pulse into two replicas, vary their relative delay, overlap them noncollinearly in a thin second-harmonic crystal, and spectrally resolve the cross-generated beam. Its propagation direction separates it from the individual beams' self-generated harmonics. For complex pulse envelope $E(t)$, the ideal trace iswhere $\Omega$ denotes the output frequency offset in the envelope convention. An iterative phase retrieval algorithm seeks a pulse consistent with both this measured Fourier magnitude and the nonlinear product relation. The delay axis provides timing structure, while the resolved spectrum adds information missing from a plain intensity autocorrelation.^[ref]

The measured trace does not fix absolute optical phase or absolute time origin. SHG FROG also has a conjugate time-reversal ambiguity: $E(t)$ and $E^{\ast }(-t)$ produce the same trace. Extra information, such as a known dispersion change and a second measurement, can resolve that direction-of-time ambiguity. Finite phase-matching bandwidth, group-velocity mismatch, spatial chirp, spectrometer calibration, delay error, noise and instability over the scan must be controlled. A thin gate helps avoid temporal blurring, but trades against signal. FROG therefore reconstructs a pulse under an explicit instrument model rather than reading optical phase directly from a single intensity image.

A phonetician studies the physical production, transmission or perception of speech. Articulatory phonetics investigates the moving vocal tract, acoustic phonetics measures recorded sound, and auditory phonetics studies listeners' responses. One research question can require evidence from more than one of these stages.

For example, a phonetician investigating a vowel contrast can record repeated tokens, estimate formants and test whether listeners distinguish the recordings. Speaker variation and analysis settings must be controlled or measured before differences are attributed to the contrast. Praat provides tools for waveform, spectrogram, pitch contour and formant analysis, making several of these observations reproducible.^[ref] The profession therefore connects language questions to instruments, explicit annotation rules and testable measurements.

Phonetics studies the physical production, transmission and perception of speech. Articulatory phonetics examines the moving structures that shape the airflow; acoustic phonetics examines the resulting sound waves; auditory phonetics examines how a listener perceives them. These are different measurements along the same communication chain.

During voiced speech, airflow from the lungs drives vocal fold vibration. Movements of the tongue, lips and other parts of the vocal tract shape the emerging sound. This separates the production of a vibrating source from the articulation of recognizable speech, and both from the language expressed by it.^[ref]

A simple acoustic comparison records the same spoken phrase twice, once as a statement and once as a question. The sound pressure time series and its spectrogram allow changes in fundamental frequency, segment duration and pauses to be compared. The comparison investigates physical differences in prosody; the written words alone do not specify those measurements.

Praat is software for analyzing, synthesizing, annotating and manipulating speech, created by Paul Boersma and David Weenink. It makes the connection between a recorded acoustic signal and measurable speech properties explicit: a waveform, a spectrogram, a pitch contour and estimated formants describe different aspects of the same recording.^[ref]

For a sustained vowel, one can compare the repeating structure of the waveform with the estimated fundamental frequency, then examine how the frequency spectrum is shaped by the vocal tract. A change in vowel quality need not be a change in pitch. Annotations can align intervals with phonemes or syllables without treating every acoustic boundary as an unambiguous linguistic boundary.

Measurements depend on the analysis settings and the signal. In particular, a displayed pitch contour can contain octave errors, while estimated formants depend on the analysis model. Inspecting the recorded sound and analysis assumptions is therefore part of the experiment, rather than accepting every displayed trajectory as ground truth.

Prosody comprises patterns of pitch, timing and emphasis extending across the individual segments of speech. Speech intonation concerns the changing pitch pattern, while speech rhythm concerns the temporal organization. The same sequence of words can be spoken with different prosody.

For acoustic analysis, a recording is examined over time. A spectrogram can reveal changes in the fundamental frequency of voiced portions; segment durations and pauses provide timing measurements. The perceived pitch and emphasis are perceptual judgments, so they should be distinguished from the measured frequency and sound pressure. Phonetics relates the recorded signal to its production and perception.

The self-gated second-harmonic spectrogram has the displayed ideal form. Its delay marginal is proportional to the intensity autocorrelation by the Parseval identity. Absolute time and wave phase are undetermined; $A(t)$ and $A^{\ast }(-t)$ also give the same record. Finite crystal acceptance and spatial walk-off modify the ideal gate.

The short-time Fourier transform analyzes the local frequency content of a signal by translating a window and then taking a Fourier transform. For a window $g$ and suitable signal $f$, one angular-frequency convention isThe time coordinate $\tau$ selects a neighborhood through the window function, while $\omega$ tests a local oscillation. The complex conjugation and Fourier normalization are part of the convention.

For $f(t)=e^{i{\omega }_{0}t}$ and an integrable window, substitution $u=t-\tau$ gives $V_{g}f=e^{-i(\omega -{\omega }_0)\tau }\hat{\overline{g}}(\omega -{\omega }_0)$. Its magnitude is centered on the tone frequency according to the window transform. A narrower time window improves temporal localization but spreads its Fourier transform, reflecting the uncentred Fourier uncertainty principle. The squared magnitude gives a spectrogram, which displays changing frequencies rather than only one whole-record spectrum.

A spectrogram displays a signal's changing local frequency spectrum, usually by color proportional to squared short-time Fourier transform magnitude. With window function $w$, one convention isThe window selects a neighborhood of time $t$ before taking its Fourier transform. A sinusoid gives a persistent frequency ridge, while a brief pulse spreads across frequencies and occupies a short time range.

A longer window separates nearby persistent frequencies more clearly but mixes events across a longer interval. A shorter window localizes transients but broadens their spectral features. Changing the window function changes this tradeoff and the spectral leakage. Zero padding can sample the displayed frequency curve more finely; it does not add observed data or restore the resolution lost through a short measurement interval. The phase is discarded in the plotted squared magnitude, so the spectrogram should not be confused with a complete set of complex transform coefficients.