Transcript No Slide Title

Physics 371 - Acoustics for Musicians
selected slides, February 28, 2002
Sound intensity Level
The decibel (dB)
Sound pressure
Examples
Sensitivity curves (Phon)
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?
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:
I
L  10 log
I0
(can be used to compare any two intensity levels
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
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
2
I 
P 



I 0 P0 
P
L  20 log
P0
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)
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.
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
Equal loudness level curves: LL= 40 phones
sound level (dB)
intensity
W/m2
Curves of equal-loudness level
press
N/m2
sound level (dB)
intensity
W/m2
press
N/m2
Good audio amplifier use automatic loudness control
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
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
0
0
0
5
10
15
ms 20
5
5
10
10
15
15
ms
ms
20
20
30dB
70dB
60dB
0
5
10
20dB
15
ms 20