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Basic Concepts: Physics
1/25/00
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Sound
• Sound= physical energy transmitted through
the air
• Acoustics: Study of the physics of sound
• Psychoacoustics: Psychological response to
acoustic stimuli (loudness, pitch & timbre)
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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
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Condensation & Rarefaction of Particles
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Particle Collision & Rarefaction
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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
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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
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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
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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
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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)
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Fourier Analysis
• Complex sounds = many sinusoids
• Amplitude Spectrum (Frequency, Amplitude,
Phase)
• Summation of sinusoidal components
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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.
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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
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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
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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
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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
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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
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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
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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
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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)
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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
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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.