Hearing Science: Basic Wave Concepts, Amplitude, Frequency, and Period

Speech Chain and Why Hearing Science Matters

• Everyday relevance: hearing science supports interactions with family (e.g., college life and routines like checking on dorm meals). Using the speech chain example, a speaker (mom) emits a waveform that the listener (student) hears and processes. The speaker also monitors her own voice via auditory feedback to adjust loudness, rate, etc., illustrating feedback loops grounded in hearing science.
• Why it matters: hearing science is a basic building block for communication sciences and disorders, audiology, and speech-language pathology.
• Slido integration: two polls and a Q&A are used to engage the class; QR code provided on slides.

Learning objectives and slide cues

• Green text (green circles): basic components of sound waves – amplitude, frequency, and period.
• Sound propagation: how sound travels through environments; differences between quiet rooms and noisy spaces (e.g., food hall).
• Orange text (perceptual components): how we perceive sounds, including frequency spectra and decibels; focus on how we interpret sounds after they’re heard.
• Note: Phase is not covered in this introductory class; emphasis is on amplitude and frequency/period.

What is sound? Two complementary definitions

• Psychological definition: sound = the sensation produced by stimulation of the auditory system; the brain lights up in auditory cortex when cochlear transduction occurs.
• Physical definition: sound = a series of disturbances of molecules within a medium (e.g., air) that propagates as a wave.
• Everyday usage often blends the two (is the tree falling a sound or a sound wave?):
  • Psychological view emphasizes the sensation of hearing.
  • Physical view emphasizes the mechanical disturbance (the wave) that travels through a medium.
• Dwight’s quip from The Office (humor used to illustrate the distinction): "a tree falling does not make a sound, it makes a sound wave" (i.e., a disturbance in the medium that may or may not be perceived as sound depending on a listener).
• Key point: sound waves require a medium, a vibrating source, and elasticity that returns particles to rest after displacement. The term "sound" can refer to the perceptual sensation or the physical wave, depending on context.

Sound as a wave in a medium

• Medium: air is the primary example in hearing science; waves propagate through air by disturbing air molecules.
• Requirements for a wave:
  • A medium through which energy travels (air, in this context).
  • A vibratory force that starts the disturbance (e.g., a loudspeaker diaphragm).
  • Elasticity: particles return to their resting state after displacement; energy is carried, but individual particles do not travel with the wave over large distances.
• Disturbance vs transport: a wave carries energy, but the medium’s particles mostly wiggle locally rather than migrating with the wave (contrast with wind moving air masses).
• Wave type note: the instructor uses a visualization of a transverse-like wave in a broad analogy, but in air, sound is typically described as a longitudinal wave with particle motion parallel to the direction of wave travel; the lecture emphasizes the disturbance and the energy transfer through the medium.
• Visualization: a red vibrating source (diaphragm) displaces nearby air molecules (blue dots), creating regions of compression (high pressure) and rarefaction (low pressure).
• Waveform concept: a graphic representation of the sound’s amplitude over time; the actual medium particles merely wiggle; the waveform is a useful abstraction for analysis.
• Compression/condensation: when the diaphragm moves outward, air molecules are pushed together, creating a high-pressure region; conversely, retracting creates a low-pressure region.
• Air pressure mapping: high-pressure regions correspond to dense clustering of molecules; low-pressure regions have fewer molecules. A time-based plot shows pressure as a function of time or distance, illustrating the wave's profile.

Waveform concepts and terminology

• Waveform: a graphic representation of a sound's amplitude as a function of time (or distance).
• Amplitude vs energy: amplitude describes the displacement magnitude of air molecules; energy is carried by the wave as it propagates.
• Amplitude-related descriptors:
  • Instantaneous amplitude: amplitude at a specific time point (e.g., a = +4 cm, b = -4 cm, c = +1 cm in the example).
  • Maximum (peak) amplitude: the largest magnitude of displacement (absolute value of the highest peak).
  • Peak-to-peak amplitude: the difference between the maximum positive peak and the maximum negative peak; useful for certain analyses.
  • Perceptual correlate: loudness or volume (how loud the sound seems).
• Common output units for amplitude: can be physical (e.g., cm of displacement) or acoustic (e.g., pressure or intensity); for this course, amplitude is often discussed in terms of sound pressure level (dB SPL) when quantifying sounds.
• Note on common practice: while amplitude can be described in several ways, the course emphasizes maximum amplitude for general descriptions and dB SPL for perceptual loudness scaling.

Perceptual correlates: pitch, loudness, and timbre

• Perceptual correlates:
  • Amplitude -> loudness (how loud the sound seems).
  • Frequency -> pitch (how high or low the sound seems).
  • Phase (not covered in depth here) influences timbre and waveform shape in more advanced analyses.
• Frequency spectra: brief introduction to how we decompose complex sounds into their frequency components (mentioned as a topic for later in the course).
• Decibels (dB SPL): the standard unit used for measuring sound amplitude in perceptual contexts; dB SPL is the reference for sound pressure level.

Frequency and periodicity: core definitions

• Frequency definition: the rate of oscillation; number of cycles per unit time.
• Oscillation: a cyclical, repeating pattern of motion.
• Cycle: one complete repetition of the waveform’s pattern.
• Periodic motion: motion that repeats itself identically over time.
• Frequency unit: hertz (Hz), where 1 Hz = 1 cycle per second.
• Perceptual correlate: pitch (how we perceive the frequency of a sound).
• Frequency equation: $f = \frac{ ext{number of cycles}}{t}$ where t is in seconds and f is in Hz.
• Example 1: If 1.5 cycles occur in 3 seconds, then $f = \frac{1.5}{3} = 0.5\text{ Hz}.$
• Example 2: If 4 cycles occur in 3 seconds, then $f = \frac{4}{3} \approx 1.33\text{ Hz}.$
• Practical note: numbers may be given in decimals; use a calculator if needed.

Practical frequency calculations with varying time units

• Example 3 (blue waveform): 3.5 cycles in 5 milliseconds (5 ms) → convert time to seconds: $t = 5\text{ ms} = 0.005\text{ s}$ → $f = \frac{3.5}{0.005} = 700\text{ Hz}.$
• Example 4 (orange waveform): 1.5 cycles in 4 seconds → $f = \frac{1.5}{4} = 0.375\text{ Hz}$; period $T = \frac{4}{1.5} = 2.667\text{ s}$.
• Converting units when needed:
  • If time is given in milliseconds, convert to seconds for the frequency formula: $t\text{(s)} = \frac{t\text{(ms)}}{1000}.$
• Example after conversion sanity check: 3 cycles in 1 second would give $f = \frac{3}{1} = 3\text{ Hz}.$
• Quick mental math tip: stick to a calculator for accuracy; units on the denominator must be seconds for frequency calculations.

Period: time per cycle and its relation to frequency

• Period definition: the time it takes to complete one full cycle of the waveform.
• Period formula: $T = \frac{t}{N<em>{\text{cycles}}}$ where t is elapsed time in seconds and N{cycles} is the number of cycles observed.
• Simple relation between f and T:
  • $f = \frac{1}{T}$
  • $T = \frac{1}{f}$
• Example: If two cycles occur in one second, then $T = \frac{1\text{ s}}{2} = 0.5\text{ s}$ and $f = \frac{1}{0.5\text{ s}} = 2\text{ Hz}.$
• Example (orange waveform recap): If something has 4 seconds between one oscillation and the next for 1.5 cycles, the period per cycle is $T = \frac{4\text{ s}}{1.5} \approx 2.667\text{ s}.$
• Example (blue waveform recap): Given 4.5 cycles and 0.007 seconds (7 ms) between measurements, convert time to seconds: $t = 0.007\text{ s}$; $T = \frac{0.007\text{ s}}{4.5} \approx 0.001556\text{ s} \approx 1.56\text{ ms}.$
  • When reporting the answer, unit consistency matters: if original time was in milliseconds, report period in milliseconds (e.g., $T \approx 1.6\text{ ms}$).

Inverse relationship and intuition

• Frequency and period are inversely related:
  • High frequency => short period.
  • Low frequency => long period.
• Summary relation: $f = \frac{1}{T} \quad\text{and}\quad T = \frac{1}{f}.$
• Conceptual check: a waveform with many oscillations in a short time has high f; a waveform with few oscillations has low f.

Worked practice: identifying frequency from cycles and time

• Problem: Given a periodic waveform, how many cycles are in one second?
  • If you count 3 cycles in one second, then $f = 3\text{ Hz}.$
• Problem: If you observe 3 cycles in 0.5 seconds, then $f = \frac{3}{0.5} = 6\text{ Hz}.$
• Problem: If you observe 2 cycles in 2 seconds, then $f = \frac{2}{2} = 1\text{ Hz},\ T = 1\text{ s}.$

Key takeaways and practical implications

• Sound is a physical wave and a perceptual phenomenon; understanding the link between physical properties (amplitude, frequency, period) and perceptual experiences (loudness, pitch) is central to hearing science.
• The two complementary definitions of sound (psychological vs physical) remind us to be precise about context: are we describing the sensation or the wave that propagates through a medium?
• In applied settings (e.g., audiology), frequency relates to pitch, while amplitude relates to loudness; decibels (dB SPL) are used to quantify amplitude in perceptual terms.
• Real-world propagation depends on the environment; quieter rooms vs noisier environments alter how sound is perceived and measured.
• The course uses a color-coded slide cue system to label concepts: green for core sound components (amplitude, frequency, period) and orange for perceptual components (spectra, loudness, pitch).

Quick reference formulas (LaTeX)

• Frequency: $f = \frac{\text{cycles}}{t}$ (cycles per second, units: Hz)
• Period: $T = \frac{t}{\text{cycles}}$ or $T = \frac{1}{f}$
• Inverse relationships: $f = \frac{1}{T}, \quad T = \frac{1}{f}$
• Example computations from lecture:
  • 1.5 cycles in 3 s: $f = \frac{1.5}{3} = 0.5\text{ Hz}$
  • 4 cycles in 3 s: $f = \frac{4}{3} \approx 1.33\text{ Hz}$
  • 3.5 cycles in 5 ms: convert to seconds $t = 0.005\text{ s}$; $f = \frac{3.5}{0.005} = 700\text{ Hz}$
  • 1.5 cycles in 4 s: $f = \frac{1.5}{4} = 0.375\text{ Hz}, \quad T = \frac{4}{1.5} \approx 2.667\text{ s}$
  • 3 cycles in 1 s: $f = 3\text{ Hz}$
• Amplitude descriptors (conceptual): instantaneous amplitude, maximum amplitude, peak-to-peak amplitude; perceptual correlate: loudness (volume).
• Units: amplitude can be in physical units (e.g., cm of displacement) or acoustic units (e.g., dB SPL for amplitude).

Notes on lecture context and clarifications

• The instructor described sound waves as transverse in an introductory context; in air, sound is typically described as longitudinal. The core idea is that air particles oscillate and energy propagates through the medium; the diagram and analogy serve as a teaching tool, but students should be aware of the distinction in real physics.
• The lecture emphasizes building intuition for how to quantify sound using amplitude and frequency, and how these relate to perceptual experiences of loudness and pitch. The concept of a waveform helps visualize amplitude over time and is foundational for subsequent topics like spectra and decibels.

Practice prompts (to test understanding)

• If you observe 3 cycles in 2 seconds, what is the frequency? Answer: $f = \frac{3}{2} = 1.5\text{ Hz}.$ Then the period is $T = \frac{1}{f} = \frac{1}{1.5} \approx 0.667\text{ s}.$
• If a waveform has a period of 0.2 seconds, what is the frequency? Answer: $f = \frac{1}{0.2} = 5\text{ Hz}.$
• A signal has 7 cycles in 0.01 seconds. What is the frequency? Answer: $f = \frac{7}{0.01} = 700\text{ Hz}.$