study guide com science

SPAU 3304 Communication Sciences

EXAM 1 STUDY GUIDE

Spring 2025

• Understand what the Newton’s Laws of Motion states

• First Law (Law of Inertia):An object will remain in its state of motion (at rest or moving with constant velocity) unless acted upon by an unbalanced force

• Second Law (Force = Mass x Acceleration):The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass, represented by the equation F = ma

• Third Law (Action-Reaction):When one object exerts a force on another object, the second object exerts an equal and opposite force back on the first object

Newton's Laws: Crash Course Physics #5

• Properties required for sound transmission:  requires a medium with properties that support the propagation of vibrational energy. The medium’s elasticity, density, and, in the case of gases, temperature, are crucial factors influencing the speed and efficiency of sound transmission.

Sound as a Mechanical Wave

• States of matter: 

Solid

Particles are tightly packed together

Particles vibrate in place, but don't move around

Solids have a definite shape and volume

Liquid 

Particles are loosely packed together

Particles flow around each other

Liquids have a definite volume, but can change shape

Gas 

Particles move freely and spread apart from one another

Gases have no definite volume or shape

• Brownian Motion (nature of sound waves): Brownian motion is the random movement of tiny particles caused by collisions with smaller molecules. Sound waves move through air by vibrating particles back and forth, creating high and low pressure areas. While sound waves move in an organized way, Brownian motion causes random particle movement at the same time.

What Is Brownian Motion? | Properties of Matter | Chemistry | FuseSchool

Velocity: The speed and direction of an object’s motion. In sound, it refers to how fast a wave travels through a medium.

Force : A push or pull on an object that causes it to move, stop, or change direction.

Pressure :The amount of force applied over an area. In sound, pressure changes create compressions and rarefactions in a wave.

Wave: A repeating disturbance that moves through a medium, transferring energy without transporting matter.

Medium :The substance (air, water, solid) through which a wave travels.

Sound:Vibrations that travel as waves through a medium and can be heard when they reach the ear.

Psychoacoustics: The study of how humans perceive and interpret sound.

•Frequency :The number of vibrations (cycles) per second in a sound wave, measured in Hertz (Hz). Higher frequency means a higher pitch.

Period: The time it takes for one complete cycle of a wave to occur, measured in seconds (s). It is the inverse of frequency (T = 1/f).

Amplitude: The height of a sound wave, which determines its loudness. Measured in decibels (dB). Greater amplitude means a louder sound.

Inertia: The tendency of an object (or air particle) to resist changes in motion. In sound, this keeps particles moving once disturbed.

Mass: The amount of matter in an object, measured in kilograms (kg). In acoustics, mass affects how sound waves travel through different materials.

Elasticity and Stiffness: Elasticity is a material’s ability to return to its original shape after being disturbed, while stiffness is how resistant it is to deformation. Both affect sound wave speed.

Oscillation : The back-and-forth motion of particles in a sound wave, creating vibrations that produce sound.

Compression (Condensation): A region in a sound wave where air particles are pushed close together, creating an area of high pressure. 

Rarefaction: A region in a sound wave where air particles are spread apart, creating an area of low pressure. 

Compression and Rarefaction class 9

Transverse & Longitudinal Waves | Waves | Physics | FuseSchool

Identifying Compression & Rarefaction on a Diagram:

• Transverse wave:  compressions correspond to the peaks (crests) where pressure is highest, while rarefactions correspond to the valleys (troughs) where pressure is lowest.

• longitudinal wave diagram: compressions appear as dense, closely packed particle regions, while rarefactions appear as spaced-out regions between compressions.

• Understand how energy propagation in sound waves: Propagation of sound" refers to the process of sound waves traveling through a medium, essentially meaning how sound moves from its source to another location by creating disturbances in the air particles, which then transfer that energy to neighboring particles, causing the sound to spread outwards as a wave; it requires a medium like air, water, or solid to travel through, and is characterized by alternating regions of compression and rarefaction within the medium

Basics of Sound Waves

o Transverse vs. longitudinal waves Transverse & Longitudinal Waves | Waves | Physics | FuseSchool

o Types of Waves in Acoustics

Traveling Waves: Crash Course Physics #17

Sinusoids (Sine Waves): The simplest type of wave, representing a single frequency with a smooth, periodic oscillation. It is the building block of all sound waves.Sine Wave | Simple Explanation on a Giant or Ferris Wheel | Trigonometry | Learnability

Pulse Waves: A type of wave with sudden changes in amplitude, often used in digital audio and square wave synthesis. These waves switch between high and low states.

Complex Waves: A combination of multiple sine waves of different frequencies, amplitudes, and phases. Most real-world sounds (voices, instruments) are complex waves rather than pure sine waves.

Waveforms – What Do They Show?:Waveforms visually represent how a sound wave changes over time. They display variations in amplitude (loudness) and frequency (pitch), showing the shape of a sound signal.

Parts of a Waveform:

1. Crest (Peak): The highest point of the wave, representing maximum compression (high pressure).

2. Trough: The lowest point of the wave, representing maximum rarefaction (low pressure).

3. Wavelength: The distance between two consecutive crests or troughs, determining frequency.

4. Amplitude: The height of the wave, indicating loudness.

5. Zero Crossing: The point where the wave passes through the centerline, moving from compression to rarefaction.

o • X-Axis (Horizontal Axis): Represents time, showing how the wave changes over a period. It is usually measured in seconds (s) or milliseconds (ms).

• Y-Axis (Vertical Axis): Represents amplitude, showing the wave’s intensity or loudness. It is typically measured in decibels (dB) or a relative unit of sound pressure.

• Understand the way sound travels through medium. What happens?

When sound travels through a medium (such as air, water, or a solid), it moves as a longitudinal wave, meaning the particles in the medium vibrate back and forth in the same direction as the wave is traveling.

What Happens When Sound Travels?

1. Vibration Starts the Wave: A sound source (like a speaker or vocal cords) creates vibrations.

2. Compression and Rarefaction Form: The vibrating source pushes air particles together (compression) and then pulls them apart (rarefaction).

3. Energy Moves, But Particles Stay: The wave moves through the medium, but the individual particles only oscillate back and forth rather than traveling with the wave.

4. Speed Depends on Medium: Sound moves fastest in solids, slower in liquids, and slowest in gases because particles are closer together in solids, allowing vibrations to transfer more quickly.

5. Wave Weakens Over Distance: As sound travels, it loses energy (attenuation), making it quieter the farther it moves from the source.

This explains why sound travels differently through different materials and why distant sounds can fade over time.

• Calculate: frequency, period,

 amplitude,

intensity (micropascals to dB SPL)

• Inverse square law:The Inverse Square Law states that sound intensity decreases as the distance from the source increases. Specifically, the intensity is inversely proportional to the square of the distance from the source.

• Understand the relationship between

1. Intensity and Amplitude

How are they related?

• Intensity measures how much energy a sound wave carries.

• Amplitude is the height of the sound wave (how strong the vibrations are).

• Higher amplitude = greater intensity.

• Doubling the amplitude makes intensity four times greater because intensity depends on the square of amplitude.

Example:

If you turn up the volume on a speaker, the sound gets louder because amplitude increases, making the intensity much stronger.

2. Intensity and Frequency

How are they related?

• Frequency is how many times per second a sound wave vibrates (measured in Hz).

• Intensity depends more on amplitude than frequency, but higher frequencies can carry more energy per cycle.

• Human ears are more sensitive to certain frequencies, so a high-frequency sound may seem louder even if it has the same intensity as a low-frequency sound.

Example:

• A 1000 Hz beep at 60 dB sounds louder than a 100 Hz hum at 60 dB, even though their intensities are technically the same.

3. Frequency and Period

How are they related?

• Frequency is how often a wave repeats in one second.

• Period is how long one cycle of the wave takes.

• They are inversely related:

• Higher frequency = shorter period (faster waves).

• Lower frequency = longer period (slower waves).

Example:

• A 1000 Hz sound completes 1000 cycles per second, meaning each cycle lasts 1/1000 seconds.

• A 100 Hz sound takes 1/100 seconds per cycle, so each wave lasts longer.

4. Sound Pressure Wave and dB SPL

How are they related?

• Sound pressure is the actual physical force of the sound waves moving through the air.

• dB SPL (decibels Sound Pressure Level) measures how loud that pressure is.

• A 10× increase in pressure = a 20 dB increase in loudness.

Example:

• A whisper is about 20 dB SPL (low pressure).

• A normal conversation is around 60 dB SPL (much higher pressure).

• A jackhammer is about 100 dB SPL, meaning its pressure is 10,000 times stronger than a whisper!

Quick Summary:

• Intensity & Amplitude → More amplitude = way more intensity.

• Intensity & Frequency → Higher frequencies carry more energy per cycle, but loudness depends more on amplitude.

• Frequency & Period → Higher frequency = shorter period; Lower frequency = longer period.

• Sound Pressure & dB SPL → dB SPL is the logarithmic measure of sound pressure, where a 10× increase in pressure = +20 dB SPL.

Properties of Sound Waves: Definitions and Units of Measurement

1. Frequency (Perceptual Correlate = Pitch): Definition: Frequency is the number of wave cycles per second. It determines how high or low a sound is perceived.

• Unit of Measurement: Hertz (Hz) → 1 Hz = 1 cycle per second

Perceptual Correlate: Pitch (higher frequency = higher pitch, lower frequency = lower pitch)

Example:

• A low-pitched bass drum sound might be 50 Hz.

• A high-pitched whistle could be 2000 Hz or more.

2. Period- Definition: Period is the time it takes for one complete cycle of a sound wave to pass.

• Unit of Measurement: Seconds (s) or milliseconds (ms)

• Formula: where T = period and f = frequency (Hz).

Example:

• A 500 Hz sound wave has a period of:

3. Intensity / Amplitude

Definition: 

 Amplitude: The height of a sound wave, representing how much pressure it has.

Intensity: The energy carried by the wave.

• Both relate to loudness.

Units of Measurement: 

Amplitude: Pascals (Pa) or Micropascals (µPa) for sound pressure

Intensity: Watts per square meter (W/m²).

• Loudness (dB SPL): Measured in decibels (dB Sound Pressure Level).

Example:

• A whisper is around 20 dB SPL.

• Normal conversation is about 60 dB SPL.

• A rock concert can reach 110+ dB SPL.

Common Changes to Sound Intensity (dB SPL)

• +6 dB SPL → Doubling sound pressure

• -6 dB SPL → Halving sound pressure

• +3 dB SPL → Doubling sound power (e.g., adding another identical speaker).

• -3 dB SPL → Halving sound power

• Moving twice as far away → -6 dB SPL (Inverse Square Law)

Example:

• A speaker at 90 dB SPL at 1 meter will be 84 dB SPL at 2 meters.

4. dB HL (Hearing Level) Definition: dB HL measures hearing ability relative to normal hearing thresholds at different frequencies.

• Reference Values: 0 dB HL is set to the average quietest sound a normal ear can hear at each frequency.

• Use: Used in audiograms to assess hearing loss.

Example:

• 0 dB HL at 1000 Hz ≈ 7 dB SPL

• Hearing loss of 40 dB HL at a frequency means that person needs 40 dB SPL above normal threshold to hear the sound.

5. Wavelength (Speed of Sound)-Definition: Wavelength is the physical distance between two peaks of a sound wave.

Formula:

where:

• = wavelength (meters, m)

• = speed of sound (343 m/s in air at room temperature)

• = frequency (Hertz, Hz)

Example:

• A 500 Hz sound has a wavelength of:

• A 1000 Hz sound has a shorter wavelength:

• Lower frequencies = longer wavelengths; higher frequencies = shorter wavelengths.

6. Phase Angle

Definition: Phase angle describes where a sound wave is in its cycle at a specific time.

• Measured in: Degrees (°), where 360° is a full cycle.

Importance:If two waves are in phase (0° difference), they reinforce each other (constructive interference).

• If two waves are 180° out of phase, they cancel each other out (destructive interference).

Example:

• If two identical speakers play the same sound perfectly in sync (0° phase difference), the sound is louder.

• If one speaker is delayed by half a cycle (180° phase difference), the sound cancels out.

Quick Summary Table

• Dynamic range of auditory system/ human ear

• Range: 0 dB SPL (threshold of hearing) to ~120-140 dB SPL (pain threshold).

• Conversational Speech: ~60 dB SPL.

• Hearing Damage Risk: 85+ dB SPL (prolonged exposure can cause damage).

• Pain Threshold: 120-140 dB SPL (jet engines, explosions).

• Most Sensitive Range: 1000-4000 Hz (speech frequencies).

• Hearing Protection: Required for prolonged exposure above 85 dB SPL.

• Given sound waveform, know how to identify amplitude (dB SPL) and frequency.

To identify the amplitude and frequency of a sound waveform, follow these steps:

1. Amplitude (dB SPL)

• Definition: Amplitude represents the loudness or intensity of the sound. In waveforms, it’s the height of the wave peaks.

• Measurement:

• Visual Analysis: Examine the vertical axis of the waveform. Taller peaks indicate higher amplitude.

• Quantitative Analysis: Use audio analysis software to measure the peak or root mean square (RMS) amplitude.

• Conversion to dB SPL:

• Amplitude measurements can be converted to decibels Sound Pressure Level (dB SPL) using the formula:

where is the measured sound pressure, and is the reference sound pressure (typically in air).

2. Frequency

• Definition: Frequency refers to the number of cycles a waveform completes per second, determining the pitch of the sound.

• Measurement:

• Visual Analysis: Count the number of complete cycles within a specific time frame on the horizontal axis.

• Quantitative Analysis: Utilize tools like Fast Fourier Transform (FFT) in audio analysis software to identify dominant frequencies.

• Calculation:

• Frequency () is the inverse of the period ():

where is the time duration of one complete cycle.

Period, Frequency, Amplitude, & Wavelength - Waves

• Given several waveforms, be able to identify waves with lower or higher frequency.

Identifying the relative frequencies of waveforms involves analyzing the number of complete cycles each wave completes in a given time period. A higher frequency corresponds to more cycles per second, while a lower frequency corresponds to fewer cycles per second.

Example Problems:

1. Comparing Two Sine Waves:

• Wave A: Completes 5 cycles in 1 second.

• Wave B: Completes 10 cycles in 1 second.

• Question: Which wave has the higher frequency?

• Solution: Wave B has the higher frequency because it completes more cycles per second than Wave A.

2. Analyzing Waveform Graphs:

• Wave C: Completes 3 cycles over a 2-second interval.

• Wave D: Completes 7 cycles over a 2-second interval.

• Question: Which wave exhibits a lower frequency?

• Solution: Wave C has a lower frequency, as it completes fewer cycles in the same time frame compared to Wave D.

3. Frequency Calculation from Time Period:

• Wave E: Each cycle lasts 0.25 seconds.

• Wave F: Each cycle lasts 0.5 seconds.

• Question: Determine the frequency of each wave and identify which is higher.

• Solution:

• Frequency of Wave E:

• Frequency of Wave F:

• Wave E has the higher frequency.

4. Visual Inspection of Waveforms:

• Scenario: You are presented with two waveform diagrams.

• Wave G: Shows densely packed cycles.

• Wave H: Shows sparsely spaced cycles.

• Question: Which wave has the higher frequency?

• Solution: Wave G has the higher frequency, as the cycles are more closely packed, indicating more cycles per second.

5. Auditory Comparison:

• Scenario: Two pure tones are played:

• Tone I: Sounds lower in pitch.

• Tone J: Sounds higher in pitch.

• Question: Which tone corresponds to a waveform with a higher frequency?

• Solution: Tone J corresponds to the higher frequency waveform, as higher pitch sounds are produced by higher frequency waves.

By practicing with these examples, you can develop a better understanding of how to identify and compare the frequencies of different waveforms.

• Given waveform or spectrum, be able to interpret what the graph, x-axis, y-axis represents.

Interpreting waveforms and spectra involves understanding the information conveyed by their axes.

1. Waveform Graphs:

• X-Axis (Horizontal): Represents time, indicating the progression of the signal over a specific duration.

• Y-Axis (Vertical): Represents amplitude, reflecting the signal’s strength or intensity at each point in time. Amplitude can be measured in various units, such as voltage, sound pressure, or decibels (dB), depending on the context.

2. Spectrum Graphs:

• X-Axis (Horizontal): Represents frequency, showing the different frequency components present in the signal. Frequency is typically measured in Hertz (Hz).

• Y-Axis (Vertical): Represents amplitude or magnitude, indicating the strength of each frequency component. This axis shows how much of each frequency is present in the signal.

Understanding these axes allows for accurate interpretation of the signal’s characteristics in both time and frequency domains.

• Know the factors that can affect sound waves – what can increase or decrease speed, frequency, amplitude of sound waves

Sound waves are influenced by various factors that can alter their speed, frequency, and amplitude.

1. Speed of Sound

The speed at which sound travels through a medium depends on:

• Medium’s Density: Sound generally travels faster in less dense materials. For instance, sound moves faster in helium than in air due to helium’s lower density. 

• Temperature: Higher temperatures increase the speed of sound. As temperature rises, molecules move more rapidly, facilitating quicker transmission of sound waves. 

• Elasticity of the Medium: Materials with higher elasticity allow sound to travel faster. 

2. Frequency of Sound

The frequency of a sound wave, perceived as pitch, is primarily determined by the source of the sound and remains constant as it travels through a medium. However, certain factors can influence frequency:

• Source Vibration Rate: Faster vibrations of the sound source produce higher frequencies.

• Doppler Effect: The relative motion between a sound source and an observer can cause a perceived change in frequency. As the source approaches, the observer perceives a higher frequency; as it recedes, a lower frequency is perceived.

3. Amplitude of Sound

Amplitude relates to the loudness or intensity of sound and can be affected by:

• Energy Input: Increasing the energy applied to the sound source raises the amplitude, resulting in a louder sound.

• Distance from Source: As sound waves propagate, their amplitude diminishes with distance due to energy dispersion.

• Medium’s Properties: Factors like humidity and temperature can influence sound amplitude.

• Complex sounds (vs. pure tone)

o Harmonic series/harmonics

o Fundamental frequency

o Spectrum plot

In acoustics, understanding the distinction between pure tones and complex sounds, as well as concepts like the harmonic series, fundamental frequency, and spectrum plots, is essential.

Pure Tones vs. Complex Sounds

• Pure Tone: A sound consisting of a single frequency, producing a sinusoidal waveform. It’s perceived as a clear, singular pitch without any additional tonal color.

• Complex Sound: A sound comprising multiple frequencies simultaneously. These can include harmonics and overtones, resulting in a richer and more textured auditory experience.

Harmonic Series and Harmonics

• Harmonic Series: A sequence of frequencies where each frequency is an integer multiple of a fundamental frequency. This series forms the basis of many musical tones and timbres.

• Harmonics: The individual components of the harmonic series. The first harmonic is the fundamental frequency, and subsequent harmonics are higher integer multiples of this fundamental.

Fundamental Frequency

• The lowest frequency of a periodic waveform, determining the pitch of the sound. All other harmonics are built upon this base frequency.

Spectrum Plot

• A graphical representation showing the different frequencies present in a sound and their respective amplitudes. The x-axis represents frequency, while the y-axis represents amplitude, allowing for visualization of the sound’s frequency components.

For a visual and auditory explanation of pure and complex tones, you might find the following video helpful:

Pure & Complex Tones

Acoustics & Sound Study Guide

This guide covers key concepts in wave interference, resonance, frequency calculations, and filtering in acoustics.

1. Interference Patterns

When two or more sound waves interact, they create interference patterns that either amplify or cancel out parts of the sound.

Constructive vs. Destructive Interference

• Constructive Interference: Occurs when two waves meet in phase (i.e., their peaks and troughs align). This results in a stronger/louder sound.

• Destructive Interference: Occurs when two waves meet out of phase (i.e., a peak aligns with a trough). This cancels out parts of the sound, reducing volume or creating silence.

🔹 Example: Noise-canceling headphones use destructive interference to eliminate unwanted sounds.

2. Formulae to Know

Frequency & Period

• Frequency (f) = Number of cycles per second (measured in Hertz, Hz)

• Period (T) = Time for one cycle (measured in seconds, s)

• Formula:

Decibel (dB) Calculations

• Sound Pressure Level (SPL):

where = measured sound pressure, and = reference sound pressure (20 µPa in air).

• Hearing Level (HL): dB HL is used in audiology, adjusted based on human hearing sensitivity.

Wavelength & Phase

• Wavelength ():

where = speed of sound (≈343 m/s in air), and = frequency.

• Phase Difference: If two waves differ by 180°, they cancel out (destructive interference).

Harmonic Series Calculation

• Fundamental Frequency (f₁): The lowest frequency of a vibrating system.

• Harmonics: Integer multiples of the fundamental frequency:

where = 1 (fundamental), 2 (second harmonic), 3 (third harmonic), etc.

3. Ratio of Decibels (dB SPL Calculation)

Decibels (dB) measure sound intensity logarithmically.

• In dB SPL calculations, the numerator is the measured sound pressure (P), and the denominator is the reference pressure (P₀ = 20 µPa in air).

• The logarithmic scale allows large differences in sound intensity to be measured effectively.

4. Resonance & Resonant Frequency

Definition of Resonance

Resonance occurs when an object vibrates at its natural frequency due to external forces, leading to an increase in amplitude.

🔹 Example: A singer breaking a glass by singing at its resonant frequency.

Calculating Resonant Frequency of a Tube

Tube Open at One End (Quarter-Wavelength Resonator)

• Formula:

where = speed of sound (343 m/s in air), and = length of the tube.

• Only odd harmonics exist (1st, 3rd, 5th, etc.).

Tube Open at Both Ends (Half-Wavelength Resonator)

• Formula:

where = length of the tube.

• All harmonics exist (1st, 2nd, 3rd, etc.).

5. Mechanical vs. Acoustic Resonance

Mechanical Resonance

• Occurs when physical structures vibrate at their natural frequency.

• Example: A bridge swaying due to wind (e.g., Tacoma Narrows Bridge collapse).

Acoustic Resonance

• Occurs when sound waves resonate inside a cavity or instrument.

• Example: The body of a guitar amplifying sound.

Difference Between Acoustic and Mechanical Resonators

• Acoustic Resonators amplify sound by vibrating air inside an enclosed space (e.g., wind instruments, vocal tract).

• Mechanical Resonators involve solid materials vibrating (e.g., tuning forks, bridges).

6. Types of Filters in Sound Processing

Filters modify the frequency content of sound.

High-Pass Filter (HPF)

• Allows high frequencies to pass and blocks low frequencies.

• Example: Used in microphones to reduce rumble.

Low-Pass Filter (LPF)

• Allows low frequencies to pass and blocks high frequencies.

• Example: Used in subwoofers to remove high frequencies.

Band-Pass Filter (BPF)

• Allows only a specific range of frequencies to pass and blocks others.

• Example: Used in radio receivers to tune into a specific station.

Band-Reject Filter (Notch Filter)

• Blocks a narrow band of frequencies while allowing others to pass.

• Example: Used to remove electrical hum (e.g., 60 Hz noise from power lines).

🔍 Summary of Key Concepts for Quick Review

📌 Final Notes for Your Study Guide

✅ Interference affects loudness and clarity in sound.

✅ Resonance amplifies certain frequencies naturally.

✅ Filters shape sound by removing or emphasizing frequencies.

✅ Understanding decibels (dB) helps measure sound intensity.

✅ Frequency, wavelength, and harmonics determine pitch and tone.

This guide should help you grasp the core principles of acoustics. Do you need more examples or practice problems?

I