The intensity level of sound 20 m from a jetairliner is 120 dB. At what distance

Question

The intensity level of sound 20 m from a jetairliner is 120 dB. At what distance from the airplane will thesound intensity level be a tolerable 100 dB? (Assume sphericalspreading of sound.) The answer was given to me as 200m.

Please Show me how you got the answer. The intensity level of sound 20 m from a jetairliner is 120 dB. At what distance from the airplane will thesound intensity level be a tolerable 100 dB? (Assume sphericalspreading of sound.) The answer was given to me as 200m.

Please Show me how you got the answer.

Explanation / Answer

we have = 10log(I/I0)    for = 120dB    120dB = 10log(I1/1.0*10-12W/m2)     or        1012 =I/1.0*10-12 W/m2     or       I1 = 1W/m2 similarly for = 100dB calculating we get          I2= 1*10-2 W/m2    similarly for = 100dB calculating we get          I2= 1*10-2 W/m2    The intensity of the sound at a distance r from the sourceis     I = Pave /4r2 Here the ratio of intensities at the two spherical wavesis       I1 /I2 =r22/r12       thus      1W/m2/1*10-2dB =r22/(20m)2       r22 =(120/100)*(20m)2 or    r2 = 200m or    r2 = 200m         

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