2.011
3/22/06
HW# 4 Solution Set
Problem 1: (10 points)
a.
(2 points)The
decibel
(
dB
) is a measure of the ratio between two quantities, and is
used in a wide variety of measurements in acoustics, physics and electronics.
While originally only used for power and intensity ratios, it has come to be used
more generally in engineering. The decibel is widely used as a measure of the
loudness of sound. It is a "dimensionless unit" like percent. Decibels are useful
because they allow even very large or small ratios to be represented with a
conveniently small number. This is achieved by using a
I
dB
=
10log
10
(
I
I
0
)
P
dB
=
10log10(
P
P
0
)
logarithm.
Intensity is I and pressure is denoted by P.
b.
(3 points)
i.
Jet engine – 130 dB @ 30 m
ii.
Car – motorcycle accelerating @ 5m = 110 dB
iii.
Whale – Blue Whale humming at 1m = 180 dB
iv.
Underwater Seismic Activity  seafloor volcanic eruption = 255 unerwater
dB @ 1m.
v.
Rock concert – average is about 100 dB
vi.
Ships propeller – Supertanker = ~127 dB in air and 190 dB in water
vii. Dolphin  208 dB in water @ 6 m.
c.
(3 points)
i.
10log
10
(A/B) = 10*(log
10
(A)  log
10
(B)) = log
10
(A
10
)  log
10
(B
10
)
ii.
10log
10
(A+B) = log
10
((A+B)
10
)
iii.
10log
10
(A
B
) = B*10* log
10
(A)
d.
(2 points)
i.
10log
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 Spring '06
 AlexandraTechet
 Speed of sound, Decibel, Directivity, Sonar

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