35. Sound from a loudspeaker, which approximates a point source, is measured to have a sound level intensity of 70 dB at a distance of
3.0 m from the speaker. What is the approximate sound power emitted by the speaker?
1.1 x 10-3 watts
To calculate power we need to use the
formula = P/A where A = 4pr2.
In this formula,
represents the intensity in watt/m2 not the sound level intensity in
decibels. So we must first convert decibels to watts/m2 using the
formula
70 = 10 log10 (/o)
7 = log10 (/o)
107 =(/o) = 107(o)
where o = 1 x 10-12
watts/m2, the threshold of human hearing = 1 x 10-5
watts/m2
Now we can use our formula for power and the fact that the
sound level intensity of 70 dB occurred when we were 3 meters from the speaker.
= P/4pr2 1 x 10-5 = P/4p(3)2 P = (1 x 10-5)36p P = 0.00113 watts
36. The sound intensity levels for a machine shop and a quiet library are 90 dB and 40 dB, respectively (a) How many times greater is the intensity of the sound in the machine shop than that in the office? (b) What is each intensity?
105 times louder
40 dB = 1 x 10-8 watts/m2
90 dB = 1 x 10-3 watts/m2
To compare the intensity of these two decibel
readings
90 - 40 = 50 dB
50/10 = 5
therefore, 90 dB is 105 times louder than 40 dB
40 = 10 log10 (/o)
4 = log10 (/o)
104 =(/o) = 104(o)
where o = 1 x 10-12
watts/m2, the threshold of human hearing = 1 x 10-8
watts/m2
90 = 10 log10 (/o)
9 = log10 (/o)
109 =(/o) = 109(o)
where o = 1 x 10-12
watts/m2, the threshold of human hearing = 1 x 10-3
watts/m2
39. At a distance of 10.0 m from a point source, the sound intensity level is measured to be 70 dB. At what distance
from the source will the sound level intensity be 40 dB?
316 m
To determine this answer, we must first know the
intensities of each of the sound level readings. Note that these values are
answers to previous questions.
70 = 10 log10 (/o)
7 = log10 (/o)
107 =(/o) = 107(o)
where o = 1 x 10-12
watts/m2, the threshold of human hearing = 1 x 10-5
watts/m2
40 = 10 log10 (/o)
4 = log10 (/o)
104 =(/o) = 104(o)
where o = 1 x 10-12
watts/m2, the threshold of human hearing = 1 x 10-8
watts/m2
Since sound obeys an inverse square law, we
can use the formula
1/2=
r22 / r12 1 x 10-5 / 1 x 10-8 = r22
/ 102 r22 = (1 x 10-5 / 1 x 10-8)
* 100
41. An orchestra plays a movement pianissimo (very softly) at an average intensity of
7.5 X 10-6 W/m2 and another movement is played fortissimo (very loudly) at
2.5 x 10-4 W/m2 What is the difference in the average sound
level intensities for the movements?
15 dB
SL = 10 log10 (7.5 X 10-6 /1
x 10-12)
SL = 10 log10 (7.5 X 106)
69 dB
SL = 10 log10 (2.5 X 10-4 /1
x 10-12)
SL = 10 log10 (2.5 X 108)
84.00 dB
84 - 69 = 15 dB
43. A person standing 4.0 m from a wall shouts so that the sound strikes the wall with an intensity of
2.5 X 10-4 W/m2 Assuming that the wall absorbs 20% of the incident energy and reflects the rest, what is the sound intensity level just before and after the sound is reflected?
84 dB and 83 dB
SL = 10 log10 (2.5 X 10-4 /1
x 10-12)
SL = 10 log10 (2.5 X 108) 84 dB
If the wall absorbs 20%, then 80% is reflected. The
reflection has an intensity of 0.80(2.5 X 10-4) = 2.0 x
10-4 watts/m2
SL = 10 log10 (2.0 X 10-4 /1
x 10-12)
SL = 10 log10 (2.0 X 108) 83 dB
46. A 1000-hz tone issuing from a loudspeaker has a sound level intensity of 100 dB at a distance of
2.5 m. If the speaker is assumed to be a point source, how far from the speaker will the sound have intensity levels of (a)
60 dB and (b) just barely enough to be heard?
2.5 x 102 m
2.5 x 105 m
To calculate this result, we must compare the intensities in watt/m2.
100 = 10 log10 (/o)
10 = log10 (/o)
1010 =(/o) = 1010(o)
where o = 1 x 10-12
watts/m2, the threshold of human hearing = 1 x 10-2
watts/m2
60 = 10 log10 (/o)
6 = log10 (/o)
106 =(/o) = 106(o)
where o = 1 x 10-12
watts/m2, the threshold of human hearing = 1 x 10-6
watts/m2
Since sound obeys an inverse square law, we
can use the formula
1/2=
r22 / r12
To compare 100 dB and 60 dB
1 x 10-2 / 1 x 10-6 =
r22 / 2.52 r22 = 2.52 (1 x 10-2 /
1 x 10-6)
r22 = 6.25 (1 x 104)
r22 = 6.25 x 104 r2 = 250 meters
To compare 100 dB and 0 dB
1 x 10-2 / 1 x 10-12 =
r22 / 2.52 r22 = 2.52 (1 x 10-2 /
1 x 10-12)
r22 = 6.25 (1 x 1010)
r22 = 6.25 x 1010 r2 = 250000 meters
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= P/A where A = 4pr2.
In this formula, 