Page 198 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 15] WAVES AND SOUND 183

the distance R 2 can be found from

I 2 R 1 2
=
I 1 R 2
2
The response of the human ear to sound intensity is not proportional to the intensity, so doubling the actual
intensity of a certain sound does not lead to the sensation of a sound twice as loud but only of one that is slightly
louder than the original. For this reason the decibel (dB) scale is used for loudness, or sound intensity level.An
2
intensity of 10 −12 W/m , which is just audible, is given the value 0 dB; a sound 10 times more intense is given
2
3
the value 10 dB; a sound 10 times more intense than 0 dB is given the value 20 dB; a sound 10 times more
intense than 0 dB is given the value 30 dB; and so forth. Formally, the sound intensity level β (Greek letter beta),
2
in dB, of a sound wave whose intensity is I,inW/m ,isgiven by
I
β(dB) = 10 log
I 0
2
where I 0 = 10 −12 W/m . Normal conversation might be 60 dB, city traffic noise might be 90 dB, and a jet
aircraft might produce as much as 140 dB (which produces damage to the ear) at a distance of 30 m. Long-term
exposure to intensity levels of over 85 dB usually leads to permanent hearing damage.
If the power input to an amplifier or other signal processing device is P in and the power output of the device
is P out , the power gain G of the system in decibels is defined as

P out
G dB = 10 log
P in
A change in audio power output of 1 dB is about the minimum that can be detected by a person with good
hearing; usually the change must be 2 or 3 dB to be apparent.

SOLVED PROBLEM 15.6

How many times more intense is a 50-dB sound than a 40-dB sound? Than a 20-dB sound?
Each interval of 10 dB represents a change in sound intensity by a factor of 10. Hence a 50-dB sound is 10 times
more intense than a 40-dB sound and 10 × 10 × 10 = 1000 times more intense than a 20-dB sound.

SOLVED PROBLEM 15.7
What is the intensity in watts per square meter of the 70-dB noise of a truck passing by?
2
7
An intensity of 0 dB is equivalent to 10 −12 W/m . Since a sound of 70 dB is 10 times more intense, it is
equivalent to a rate of energy flow of
2
7
I = (10 )(10 −12 W/m ) = 10 −5 W/m 2
SOLVED PROBLEM 15.8
A certain person speaking normally produces a sound intensity level of 40 dB at a distance of 1.0 m. If
the threshold intensity for reasonable audibility is 20 dB, how far away can the person be heard clearly?
A change of 20 dB in sound intensity is equivalent to a ratio of 10 × 10 = 100. Hence

R 2
I 2 1
= 2
I 1 R
2

√
I 1
R 2 = R 1 = (1.0m) 100 = 10 m
I 2