Basic Concepts: Physics

1/25/00

Sound

• Sound= physical energy transmitted through

the air

• Acoustics: Study of the physics of sound

• Psychoacoustics: Psychological response to

acoustic stimuli (loudness, pitch & timbre)

Wave Motion

• Sound Wave: transfer of energy through a medium

– Particles attached and interconnected

– Collide to transmit energy (condensations)

– Rarefaction: particle separation

– Longitudinal waves: back & forth motion of

particles

• Slinky

Condensation & Rarefaction of Particles

Particle Collision & Rarefaction

Sinusoid

• Projected, uniform circular motion or simple harmonic motion

• Motion produced by constant velocity

• Specified by: Frequency, amplitude & phase

– Frequency: rate of vibration of sound

– Amplitude: magnitude of vibration

– Phase: point on the sinusoidal function which the

waveform commences

Frequency

• Increased frequency= more cycles per second– Frequency- # of vibrations per second– Hertz

– One cycle of vibration = period (t0)

– f=1/t0 and t0=1/f

• 1000 Hz = 1 ms

• 100 Hz = 10 ms

• The lower the frequency of vibration, the longer the time needed for a complete cycle of vibration

Frequency

• Woman= 240 Hz, What is the period?• 4.2 ms

• Man= 120 Hz, What is the period?• 8.3 ms

• Human hearing: frequency range=

15- 20,000 Hz

Harmonic

• Integer relations among elements– Related to one another:

• series- 2nd is 2x the frequency of the first etc.

100 Hz 200 Hz 300 Hz

•Octave is a 2:1 relation between two sounds•440 Hz & next octave 880 Hz

Amplitude

• Magnitude of displacement of a sound wave

• Types of magnitude:

– Intensity- Sound energy per second over an area

of 1 square meter

– Sound Pressure Level- Amount of force per unit

area

• Both expressed on a logarithmic scale (decibel)

Fourier Analysis

• Complex sounds = many sinusoids

• Amplitude Spectrum (Frequency, Amplitude,

Phase)

• Summation of sinusoidal components

Signal to Noise Ratio

• Relative intensity of a signal compared to the

intensity of the background noise (S/N).

• Large positive values = Strong signal

• Small positive & Negative values= noise meets or

exceeds the signal

• Human voice also has noise elements.

Resonance

• Occurs when a vibrating system is driven by a periodic force at the natural frequency of the system.– Frequency-dependent

• Examples:– Cars on a bridge, regular intervals, sway of

bridge

– Glass resonates when running your finger over the rim at a certain rate

Resonance

• External, periodic, driving force creates vibration in a physical object– Vibration occurs because external force has the

same frequency

– Additive to natural frequency of object

• Can determine the natural frequency of an object:– Mass, length, & tension

Damping

• Sound energy is propagated & dissipated as it moves

• Damping = The diminution of amplitude of vibration due to friction (resistance)– Energy dies out– Related to bandwidth (frequency range of energy of

the sound)• Large bandwidth = wide range of frequencies

• Narrow bandwidth = small range of frequencies

• Larger bandwidth = more damping

Reverberation

• Opposite of damping

• Sounds reverberate or move

• Bounce back and forth from wall to wall

• Echoes that are not damped to inaudibility

within 50 ms can interfere with the next

sound

Applied Mathematics

• Estimation of loudness does not change

linearly to the physical increase in intensity

– Human judgment of pitch is nonlinear

– Range of perception is great (scale is large)

– Transforming a number scale to convenient

range

Logarithms

• Number expressed as a power of 10 or

natural log

– ex. 100 is 102 (10 to the 2nd power)

– 10 is the base and 2 is the exponent

Bel

• Strength or magnitude of sound expressed in decibel’s

• Bel = logarithm of a ratio– Useful to express large #’s of intensities that the ear

responds to.

– Ratio: intensity of any given sound (I1) is compared to a reference intensity (I0)

– The bel is a log to the base 10 of an intensity ratio

• N (bels) = log10 I1/I0

Decibel

• Because the bel is such a large unit, the

decibel was introduced

• Decibel = 1/10 of the ratio of the bel

• Decibel: N (dB) = 10 Log10 I1/I0

– ex. I1 were 1,000 times as great as I0 the power

ratio = 1,000; the dB would be 30 (log to the base

10 or 1,000 is 3 & 10 x 3=30)

Sound Pressure Level

• Used as a measure of sound in speech & hearing:– most measurement devices respond to sound

pressure (ear & microphones)

– SPL is also determined by a ratio

– Reference pressure is equal to 20 Pa

• SPL (dB)= 20 Log10 P1/P0

= 20 Log10 P1/20 Pa

• Hearing ranges = 140 dB

Readings

• Copies of readings on reserve in the library:– First reading for Feb 3 (also available in the

text: Respiratory Function in Speech and Song.