PEP Conceptual PhysicsClass Notes

Unit 7 – Vibrations, Waves, and SoundChapter 20 – Sound

Section 20.1• Properties of Sound

• Frequency of Sound

• Loudness of Sound

• Speed of Sound

• Doppler Effect

• Recording Sound

Frequency of Sound• Pitch – the perceived frequency of a sound

• Frequency and Pitch• Frequency is measured in Hz

• Pitch is described as “high” or “low”

• Human beings can detect is about 20 Hz to 20,000 Hz

• Cats – up to 85,000 Hz; bats – up to 120,000 Hz; dolphins – up to 200,000 Hz

• More when we get to human voices and musical instruments further down

Loudness of Sound• Decibels – unit for measuring loudness of sound

• A logarithmic (multiplicative) scale

• 20 dB higher means 10 times the loudness or intensity

• Most sounds are between 0 and 100 dB• 0 dB is normal limit of perception

• 100 dB is a loud audio device or musical instrument

• 120 dB is the usual threshold of pain and damage

• Sensitivity• The human ear is most sensitive to frequencies from

about 500 Hz to 5,000 Hz

• Above or below this range requires more sound intensity for the same perceived loudness

Loudness of Sound• Acoustics – the science and technology of how

sound behaves

• Libraries are “quiet” zones

• Recording studios block external sounds

• Concert halls, auditoriums, and sanctuaries amplify sound from the stage and dampen sounds from other areas

• Whisper galleries – oval (elliptical) area where a people at each foci can hear each other while whispering and no one else can hear them (cool!)

Speed of Sound• Subsonic – motion slower that the speed of sound

• Supersonic – motion faster that the speed of sound

• Shock Wave – “piled up” of wavefronts in front of a supersonic object

Source: Universal Science Source: Quartz Media

Doppler Effect• Doppler Effect – the shift in frequency caused by

the relative motion of the sound source and the observer

• Emergency vehicle’s siren as it passes you• Speed of sound remains constant (343 m/s)

• When the relative motion is toward each other, the wavelength decreases and frequency increases

• When relative motion is away from each other, the wavelength increases and frequency decreases

• Police speed detection radar uses this• See sidebar on page 473

Doppler Effect

Source: Google Sites

Recording Sound• Before the 1950s, there was no sound recording

• Audio recording in the 1950s recorded sound using analog signals on magnetic tape• Very high fidelity of sound in range of human hearing

• Modern recording is fully digital• Analog-to-digital conversion technology

• Sampling rate of 44,100 per second

• Sampled amplitude level is 16-bits (0 to 65,536)

• Recording media: CDs, DATs, and bit streams (MP3)

• Playback reverses the process• Digital-to-analog conversion technology

Recording Sound

Source: The Music Telegraph

The higher the sampling rate, the higher (and better) the sound quality.

Sampling at 44.1 kHz provides above 20 kHz human hearing upper limit.

Section 20.2• Sound Waves

• Sound and Air Pressure

• Wavelength of Sound

• Interactions

• Standing Waves and Resonance

• Fourier’s Theorem

Sound and Air Pressure• Sound travels by pressure

• Longitudinal waves spreading in circles from its source

• Alternating regions of high and low pressure

• Air pushing on adjacent molecules increases pressure

• Air between higher pressure regions is lower pressure

• Speaker cones vibrate air back and forth

Sound and Air Pressure

Source: Pro Sound Web

Sound and Air Pressure• Sound speed depends on material

• Light gases are faster than heavy – helium (965 m/s)

• Liquids are faster than gases – water (1,530 m/s)

• Solids are faster than liquids – steel (5,940 m/s)

• Sound speed depends on temperature• Molecules move slower in cool air, so sound is slower

• Molecules move faster in warm air, so sound is faster

• Sound speed depends on pressure• Molecules are farther at low pressure, so sound is slower

• Molecules are closer at high pressure, so sound is faster

Sound Wavelength• Sounds waves follow the relationship between speed,

frequency, and wavelength• Higher frequency means shorter wavelength

• Lower frequency means longer wavelength

• Musical instruments shape the sound waves• Frets on guitars, violins, and cellos

• Valves on French horns, trumpets, and tubas

• Finger holes on flutes and piccolos

• Long path → long wavelength → low frequency

• Short path → short wavelength → high frequency

Sound Interactions• Reverberation – multiple echoes of sound caused

by reflections building up and blending together

• Sounds refract, reflect, diffract, and absorb• Refraction often distorts the sound

• Reflection causes echoes and reverberation

• Diffraction allows us to hear around obstacles

• Absorption deadens sound with curtains or wall covers

• Concert halls are designed with all these in mind

• Ultrasound of babies uses high-frequency (100 kHz) sound with combined refraction and absorption

Standing Waves and Resonance• Musical instruments work by standing waves and

the fundamental frequency with its harmonics

• Both ends closed (stringed instruments)• Both ends are nodes

• Frequencies are half-wavelengths

• One end closed and one open (horns, pipes, organ)• One end is a node and one an antinode

• Frequencies are odd quarter-wavelengths

• Both ends open (woodwinds, flutes)• Both ends are antinodes

• Frequencies are half-wavelengths

Standing Waves and Resonance

Source: Timaru Girls HS (New Zealand)

Fourier’s Theorem• Fourier’s Theorem – the creation of complex waves

by adding multiple single-frequency waves• Joseph Fourier (France, 1768-1830)

Source: Harvard University

First five waves added to approximate a square wave with single-frequency sine waves.

Section 20.3• Sound, Perception, and Music

• Complex Sound Waves

• Frequency Spectrum

• Hearing Sound – The Ear

• Music

• Consonance, Dissonance, Beats

• Human Voice

• Musical Instruments

Complex Sound Waves• Normal sounds are complex and made of many

frequencies combined into one sound

• Analogy to reading• We learn to recognize words from individual letters

• We use grammar to understand sentences from words

• We use logic to understand paragraphs from sentences

• Our brains are living Fourier filters• We learn to recognize patterns of frequencies

• Musical instruments, human voices, and other sounds

• Remember when you first heard a new sound?

• You learn the sound pattern to recall it later

Frequency Spectrum• Wave forms show air pressure vs time

• See figure 20.15 (top) on page 482

• Frequency Spectrum – graph showing distribution of different frequencies in a complex sound• They graph the amplitude vs the frequency

• See figure 20.15 (bottom) on page 482

• Sonogram – graph showing how the loudness of frequencies changes over time• They graph the loudness of frequency vs the time

• Loudness is color-coded (soft=red; loud=yellow)

• See figure 20.16 on page 482

Hearing Sound – The Ear• The ear is a marvelously complex organ created by

God to allow us to hear and enjoy His creation

• Wide range of frequencies (20 to 20,000 Hz)

• Wide range of loudness (0 to over 120 dB)• That’s a 1 to 1,000,000 ratio of sound energy

• The non-linear scale protects the ear

• How we hear• Eardrum first picks up the vibrations

• Bones transmit the vibrations to the cochlea

• Cochlea converts the vibrations to brain signals

• Hearing loss occurs from loud noises and aging

Hearing Sound – The Ear

Source: 123 RF

Music• Rhythm – organization of sound into regular time

patterns

• Octave – the interval between a frequency and twice that frequency

• Note – musical sound such as from a musical scale

• Musical Scale – a series of frequencies arranged in a special (and recognizable) pattern• Most western scales have 12 semitones per octave

• Most eastern scales have 8 semitones per octave

Consonance, Dissonance, Beats• Beat – oscillation of amplitude that results from the

interference or sound waves with frequencies that are near but not equal• Useful for tuning instruments

• Consonance – a combination of sound frequencies that is agreeable or harmonious• Feelings of balance or comfort

• Examples: octave (C to C) or perfect fifth (C to G)

• Dissonance – a combination of sound frequencies that is discordant or unsettling• Feelings of tension or drama

• Examples: major second (C to D) or major seventh (C to B)

Beats

Source: The Physics Classroom

C.I. = constructive interference

D.I. = destructive interference

The beat frequency is the difference between the frequencies of the two source waves.

Human Voice• The human voice is a complex sound created by

and given by God to help us communicate• To praise God before others

• To converse with one another

• How the voice produces words• The larynx contains folds of stretchable and expandable

tissue called the vocal cords

• Air passing over and through the folds vibrate and create sound waves

• Words and sounds are formed by the shapes of the throat, mouth, and nasal cavity

Human Voice

Source: National Cancer Institute

Nasal Cavity

Musical Instruments• A normal acoustic guitar has six strings stretched

tightly to vibrate at different frequencies• The lengths of the strings can be altered by using frets

• A guitar string produces a fundamental frequency and its harmonics in a particular combination

• This combination (or recipe as the book calls it) of frequencies is the timbre• A guitar’s timbre differs from the timbre of a piano or

harpsichord (or any other instrument)

Musical Instruments - Timbre

Source: Sensation and Perception