The inverse-square law says that the intensity that you hear/measure of a sound

Question

The inverse-square law says that the intensity that you hear/measure of a sound changes depending on how far away you are from the sound source. More precisely, it is inversely proportional to the square of the distance from the sound source. That is, I 1 d 2 , (1) where I is the sound intensity and d is the distance. (This law ignores things like reflections from walls in a room; it’s most appropriate for a sound source in the open outdoors, or in a room where the walls don’t reflect much.) *ANSWER THIS QUESTION CLEARLY AND SHOW EVERYSTEP

(a) If a jackhammer 50 feet away has a sound level of 95 dB, what is the sound level (in dB) at 500 feet?

(b) What is the sound level (in dB) at 1 mile? Can you hear the jackhammer at this distance?

(c) What is this sound intensity for your answer in (b), in W/m2 ?

Explanation / Answer

a)Given,

r1 = 50 ft ; I = 95 dB ; r2 = 500 ft

I = 95 dB = 0.0032 W/m^2 [using, I(dB) = 10 log 10(I/I0)]

I = P/A

I1 = P1/A1 = P/4 pi 50^2

I2 = P/4 pi 500^2

I1/I2 = P/4 pi 50^2 x 4 pi 500^2/P = 100

I2 = I1/100 = 0.0032/100 = 0.000032 = 3.2 x 10^-5 W/m^2 = 75 dB

Hence, I2 = 75 dB

b)1 mi = 5280 ft

I1/I2 = P/4 pi 50^2 x 4 pi 5280^2^2/P = 11151.36

I2 = I1/11151.36 = 0.0032/11151.36 = 2.87 x 10^-7 W/m^2 = 54.58 dB

Hence, I2 = 54.58 dB

c)I2 = 2.87 x 10^-7 W/m^2

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.