At point A , 4.00 m from a small source of sound that is emitting uniformly in a

Question

At point A, 4.00m from a small source of sound that is emitting uniformly in all directions, the intensity level is 51.0dB .

A: What is the intensity of the sound at A?

Answer: I=        W/m^2

B: How far from the source must you go so that the intensity is one-fourth of what it was at A?

Answer: R1=       m

C: How far must you go so that the sound level is one-fourth of what it was at A?

Answer: R2=       m

D: Does intensity obey the inverse square law? yes? no?

E: Does intensity level obey the inverse square law? yes? no?

Explanation / Answer

a)
B = 10dB*log(I/Io)

here, Io = 10^-12 W/m^2

51 = 10*log*(I/Io)


==> I = Io*10^5.1

= 10^-12*10^5.1

= 1.259*10^-7 W/m^2

b)

I1/I2 = r2^2/r1^2

I1/(I1/4) = r2^2/r1^2

4 = (r2/r1)^2

r2 = 2*r1

= 2*4

= 8 m

c) B1 = 51 dB

B2 = 51/4 = 12.75 dB


B1 - B2 = 10*log*(I1/Io) - 10*log(I2/Io)


51 - 12.75 = 10*log(I1/I2)

38.25 = 10*log(r2^2/r1^2)

38.25 = 20*log(r2/r1)

log(r2/r1) = 1.9125

r2 = r1*10^1.9125

= 4*10^1.1925

= 62.3

D) Yes

E) no

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