Physics 371 Acoustics for Musicians

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Physics 371 - Acoustics for Musicians
selected slides, February 28, 2002
Sound intensity Level The decibel (dB) Sound
pressure Examples Sensitivity curves (Phon)
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Hearing loudness
Sound Intensity Level I level I is measured by
power/m2 (Watt/m2 W/m2) range from hearing
threshold to pain level intensity level at
threshold of hearing I 0 10 -12
W/m2 intensity level at threshold of pain
1 W/m2 (expressed in sound
pressure, threshold is 2x 10-5 N/m2, which
is about 1/10,000 of pressure of sheet of paper
on table) If we measure intensity of sound in
relation to threshold intensity the answer will
vary from 1 to 1,000,000,000,000 !! How can an
organism accommodate this huge intensity
range? How can we better express the intensity
level?
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Answer logarithmic response of the ear
Ear and brain is made such that equal factors
in intensity cause equal increments in
loudness.
if we call threshold intensity 1

Intensity I 1 10 102 103 104 ..1010
1011 1012


log I 0 1 2 3 4..
10 11 12
10log I 0 10 20 30 40 100
110 120 dB
this is the DECIBEL SCALE of Sound Intensity
Level
Intensity level in dB
(can be used to compare any two intensity levels
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What does one dB change in loudness sound like?
demo 1 dB steps 3 dB steps 5 dB steps
examples a) calculate the intensity ratio for a
1 dB step. b) one dynamic step (ppp - pp - p - mf
- f - ff - fff) about 6dB find intensity
ratio for each step.
comments on buying audio equipment
flatness of response, power, freq. rolloff
Adding sounds DO EXAMPLES ON BLACKBOARD
example add 440 Hz tones of 60dB and 70dB
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How is sound pressure P (N/m2) related to
intensity I (W/m2) ?
When sound PRESSURE P doubles, sound INTENSITY I
quadrupes I is proportional to P2
can use relation to calculate relative sound
pressure P2/P1 To calculate absolute sound
pressure one uses P0 2x10-5 N/m2
example if f (forte) 70dB, find sound
pressure (Answ 0.06N/m2)
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EXAMPLES (similar to homework)
example 1 a cellist can change the string
amplitude between 0.1mm and
4mm. We can assume that sound pressure is prop.
to string amplitude. What is her
dynamic range in dB?
example 2 if a crescendo from f to ff increases
the sound level by 6 dB find
the relative sound intensity
find the relative sound pressure

example 3 calculate the sound pressure for a
70dB tone (forte) (for
comparison normal athmospheric press - 105 N/m2)
example 4 calculate the intensity level in dB
when you add sounds of 65dB
and 70dB.
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Sensitivity of ear as a function of frequency
loudness level in Phons
tones of different frequencies have the same
number of phones if they sound equally loud.
the comparison tone is a 1000 Hz tone. example
If a 1000 Hz tone has intensity level of 60 db it
is said to have 60 phones - any other equally
loud pure tone of different frequency also has 60
phones. highest sensitivity of ear for about
2000 - 5000 Hz DEMO decrease sound press for
100Hz and for 2000Hz tones by same factor (same
dB) - 100Hz becomes inaudible
Application HiFi volume control vs loudness
control
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Equal loudness level curves LL
40 phones
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Curves of equal-loudness level
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Good audio amplifier use automatic loudness
control
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Neural Response of Ear the Neural Transmitters
anatomy of the ear Show overhead transparencies
(see Fig. 1 p. 88 Backus) Basilar membrane length
about 35 mm 3.5 mm per ocatave
30,000 receptors. Localization of
freq.

• sound is transmitted to the brain not as a
• wave shape but as individual pulses
  ("discharge"
• of nerve cell).
• Pulses have same height independent of stimulus,
  
• average pulse rate depends on loudness level.
• time distribution of pulses encodes wave shape

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Rose et al. J. Neurophysiology
time interval between nerve impulses for
different frequencies.
rate 30 spikes/s at 70 dB
rate 120 spikes/s at 70 dB
217 Hz
600 Hz
192 Hz
460 Hz
167 Hz
365 Hz
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30dB
70dB
60dB
20dB