Physics 371 - Acoustics for Musicians selected slides, February 28, 2002
Sound intensity Level
The decibel (dB)
Sound pressure
Examples
Sensitivity curves (Phon)

Sound Intensity Level I : level I is measured by power/m 2 (Watt/m 2 = W/m 2 ) range from hearing threshold to pain level : intensity level at threshold of hearing: I
0
=10
-12
W/m 2 intensity level at threshold of pain: 1 W/m 2
(expressed in sound pressure, threshold is 2x 10 -5 N/m 2 , 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 10 2 10 3 10 4 ……..10
10 10 11 10 12 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: L

I
I
0
(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/m 2 ) related to intensity I (W/m 2 ) ?
When sound PRESSURE P doubles, sound INTENSITY I quadrupes: I is proportional to P 2
I
I
0



P
0


2
L

P
P
0 can use relation to calculate relative sound pressure P
2
/P
1
To calculate absolute sound pressure one uses P
0
= 2x10 -5 N/m 2 example: if f (forte) = 70dB, find sound pressure (Answ: 0.06N/m 2 )

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 - 10 5 N/m 2 ) 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

Curves of equal-loudness level intensity press
W/m 2 N/m 2

intensity press
W/m 2 N/m 2
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 120 spikes/s at 70 dB
600 Hz rate 30 spikes/s at 70 dB
217 Hz
192 Hz
460 Hz
167 Hz
365 Hz
0 5 10 15 ms 20

70dB
60dB
0 5 10 15 ms 20
30dB
20dB