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: (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 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

Curves of equal-loudness level N/m2 W/m2 intensity press sound level (dB) Curves of equal-loudness level

Good audio amplifier use automatic loudness control N/m2 W/m2 intensity press sound level (dB) 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 5 10 15 20 ms 5 10 15 20 ms 5 10 15 20 ms

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