CSD 202 Week 3a Gibbs

Class Overview

• Course: CSD 202: Normal Aspects of Hearing

• Instructor: Prof. Bobby Gibbs

• Contact: bgibbs5@wisc.edu

• Department: Communication Sciences and Disorders, University of Wisconsin–Madison

• Date: Spring 2025, Week 3a

Summary of Previous Lecture

• Sound as fluctuations in pressure

• Sound travels as a longitudinal wave

• Waves are disturbances in a medium (e.g., air)

• A medium: material that possesses mass/stiffness and supports vibratory motion

Parameters of Sound

• Described using the same principles as Simple Harmonic Motion (SHM)

  • Formula: sin²θ + …

  • Pressure: measured in Pascals (Pa)

  • Period (T): T = 1/f (Time in seconds)

  • Amplitude (A): the size of the wave

  • Frequency (f): number of cycles per second

  • Phase (ϕ): indicates the speed and position within the cycle

Characteristics of Sound

• Sound represented by SHM characteristics

  • Vibratory motion needing a medium

  • Fluctuations in pressure as a longitudinal wave

  • Quantified by amplitude, frequency (1/T), and phase

  • Visualized using waveforms on a 2D plane

Relationship Between Frequency and Period

• Reciprocal relationship: f = 1/T

• Halving T → Frequency doubles

• Example calculations:

  • T = 250 ms → f = 4 Hz

  • T = 100 ms → f = 10 Hz

  • T = 10 ms → f = 100 Hz

  • T = 2 ms → f = 500 Hz

  • Encourage practice calculations to master concepts.

Duration of Tones

• Example calculation for 1000 Hz tone over 500 cycles:

  • T = 1/1000 s = 0.001 s (1 ms per cycle)

  • Duration = 500 cycles × 0.001 s = 0.5 s

  • Practice with: 2000 Hz tone x 500 cycles, etc.

Learning Objectives & Class Goals

• Understand characteristics and propagation laws of sound

• Apply knowledge to everyday sound behavior

• Today’s goals:

  • Learn sound measurement units

  • Calculate effects of distance on sound measurements

  • Understand summation of multiple sound sources

Quantification of Sound

• Agenda topics:

  • Sound power, intensity, pressure

  • Relationship among them

  • dB scale usage

  • Effects of distance on sound measurement

  • Understanding Hearing Level and Signal-to-Noise Ratio (SNR)

Power, Intensity, and Pressure Concepts

• Heater Analogy:

  • Temperature → Sound Pressure (Pa)

  • Heater Power → Sound Power (Watts)

  • Heat Flow → Sound Intensity (Watts/Area)

Sound Definitions

• Sound Power: Total acoustical energy from a sound source

• Sound Intensity: Acoustical energy per area

• Sound Pressure: Force at a point in space

Measurement Units for Sound

Explanation of Power, Intensity, and Pressure

• Power (P): Energy transferred per unit time (measured in Watts)

• Intensity (I): Power per area based on a spherical wave model: I = P/(4πr²)

  • Intensity decreases with distance, following inverse-square law.

Sound Intensity and Pain Thresholds

• Examples of absolute sound intensity (W/m²) for various situations:

  • Jet aircraft (50 m away): 102 W/m²

  • Chainsaw (1 m away): 0.1 W/m²

  • Threshold of hearing: 10⁻¹² W/m²

• Reference value for intensity calculations: Iref = 10⁻¹² W/m²

Decibels and Sound Intensity

• Decibel Scale: Logarithmic scale to compare sound levels

• Calculation of Sound Intensity Level: dB IL = 10 log(Ix/Iref)

• Understanding the significant differences between absolute sound intensity and relative measures.

Relative Sound Intensity Levels

• Examples:

  • Jet aircraft: 1014 relative to the hearing threshold.

  • Vacuum cleaner: 10⁻⁵ W/m², 70 dB

• Understanding significance of 0 dB HL and SPL does not indicate no sound.

Adding Intensities from Multiple Sources

• Equal sources example:

  • Total Sound Intensity Level (dB IL) calculation:

  • dB IL = dBx + 10 log(N) where N = number of sources

  • Unequal sources require conversion to absolute levels first before addition.

Measuring Sound: RMS and Pressure

• RMS Sound Pressure: crucial for accurate pressure and loudness representation

• Instantaneous pressure should be used for calculations due to differential phase values.

Sound Pressure Level vs. Intensity Level

• Conversion between SPL and IL:

  • SPL = 20 log(px/pref)

  • Comparisons at crucial thresholds, e.g., Threshold of hearing and discomfort.

Effects of Distance on Sound Levels

• SPL decreases at -6 dB for each doubling of distance due to 1/r relationships.

• Understanding the significance of initial pressure/intensity at specific distances.

Hearing Level (dB HL)

• Used for audiometry to express thresholds relative to average population.

• dB HL helps in standardizing measurements across frequencies for hearing assessment.

Summary Points

• Decibels serve to express relative differences in sound intensity and pressure clearly.

• Notable relationships:

  • Doubling distance → -6 dB decrease

  • Sound intensity increases → sound pressure increases; equivalence preserved across scales.

• Important to recognize SPL vs. IL for accurately representing sound in practical scenarios.

Next Class

• Reading: Plack 2.3-2.6 (spectra, complex tones/harmonics, AM/FM)

• Watch lecture video on Complex Signals (available on Canvas).