physics problem about power

Derek Lee

2010-04-06 5:35 am

a)The sound intensity level of a lawnmower engine is measured to be 90dB
at a distance of 5m. At what distance will the intensity level be measured
up to 75 dB?

b)A speaker that has an area of 60 m^2 produces the sound intensity level
equal to 80 dB. What is the power output of the speaker?

回答 (1)

天同

2010-04-06 7:28 am

✔ 最佳答案

(a) since db = 10[log(I/Io)]
where I is the intensity of sound, and Io is the threshold of hearing, generally taken to be 10^-12 w/m2

hence, 90 = 10.[log(I/Io)]
i.e. I = (Io) x 10^9

Suppose the sound intensity at distance d is 75 dB, then
I' = (Io) x 10^7.5
where I' is the sound intensity at distance d.

The intensity of sound follows the inverse square law,
I/I' = (d/5)^2
i.e. (Io).10^9/(Io).10^7.5 = d^2/25
solve for d gives d = 28.1 m

(b) Intensity of sound produced by the speaker
= (Io).10^8 =10^-12 x 10^8 w/m2 = 10^-4 w/m2

Hence, power output = 10^-4 x 60 w = 6 x 10^-3 w = 6 mw

[note: a speaker of area 60 m^2, which is about the size of a moderate flat in Hong Kong...is this realistic?]

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