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# Set9-Ave.pdf

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McMaster University

Physics

PHYSICS 1L03

Reza Nejat

Fall

Description

Phys 1L03 Tutorial session Set 9
Ninth Set - Loudness of Sound
Sound Intensity level
• The base-10 logarithm is used often in Physics, such as to define the sound intensity
level.
• The logarithm unit of sound intensity level is called the decibel (dB).
• The base-10 logarithm is used to determine the sound intensity level in decibels
(dB), which is a kind of measure of the loudness of the sound.
• The sound intensity level, β, in dB (decibel) is defined as: β = 10 log I (dB)
I
0
Where:
I is the intensity of sound inWatt /square meter (W /m ) 2 and
−12 2
I 0 10 W /m , which it is the minimum sound intensity (called the threshold intensity).
Examples:
1. Determine the sound intensity level at a point where the sound intensity is
−4 2
I = 10 W /m
I −4 2 −12 2
β = 10 log I = 10 W /m , I 0 = 10 W /m , β = ?
I0
−4 2
β = 10 log I = 10 log 10 W m/ = 10log(10 )8
I 10 −2 W m 2
0
β = 10(8 dB) = 80 dB
2. The sound intensity level at a point is 91.0 dB. What is the sound intensity at that point?
−12 2
β = 91.0 dB I0 = 10 W /m I = ?
β = 10 log I I
I ⇒ β /10 = log
0 I0
I
⇒ = inv log (β /10)
I0
I
⇒ = inv log (β /10) = inv log(91/10) = inv log(9.1)
I0
⇒ I = inv log(9.1) = 10 9.1= 1.26 × 10 W /m 2
I
0 −12 2 9 2 −3 2
I = (10 W /m ) ×1.26 ×10 W /m =11.3×10 W /m
−3 2
I = 11.3×10 W /m Phys 1L03 Tutorial session Set 9
Ninth Set- Sound intensity level
1. What are the int– 12ty le2els of sounds with intensities of
a. 1.0 ×10 W/m (1 W = 1 J/s)
– 6 2
b. 5.0 ×10 W/m
– 12 2
I0 = 1.0 ×10 W/m IL (dB) = 10 log (I / I 0
2. At a busy street corner, the sound intensity level is 78 dB. What is the intensity of
sound there?
I = 1.0 ×10 – 12W/m , IL (dB) = 10 log (I / I ),
0 0
Δ(IL) = IL 2– IL 1 10 log (I / 2 ) 1
3. How does the intensity level of a sound change if the intensity of the sound is
doubled?
– 12 2
I0= 1.0

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