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Physics-

General

Easy

Question

Intensity level 200 cm from a source of sound is $80 blank d B.$ If there is no loss of acoustic power in air and intensity of threshold hearing is $10 to the power of negative 12 end exponent W m to the power of negative 2 end exponent$ then, what is the intensity level at a distance of 4000 cm from source

Aero
54 dB
64 dB
44 dB

The correct answer is: 54 dB

$I proportional to fraction numerator 1 over denominator r to the power of 2 end exponent end fraction rightwards double arrow fraction numerator I subscript 2 end subscript over denominator I subscript 1 end subscript end fraction equals fraction numerator r subscript 1 end subscript superscript 2 end superscript over denominator r subscript 2 end subscript superscript 2 end superscript end fraction equals fraction numerator 2 to the power of 2 end exponent over denominator open parentheses 40 close parentheses to the power of 2 end exponent end fraction equals fraction numerator 1 over denominator 400 end fraction rightwards double arrow I subscript 1 end subscript equals 400 I subscript 2 end subscript$
Intensity level at point $1 comma blank L subscript 1 end subscript equals 10 log subscript 10 end subscript invisible function application open parentheses fraction numerator I subscript 1 end subscript over denominator I subscript 0 end subscript end fraction close parentheses$
and intensity at point $2 comma blank L subscript 2 end subscript equals 10 log subscript 10 end subscript invisible function application open parentheses fraction numerator I subscript 2 end subscript over denominator I subscript 0 end subscript end fraction close parentheses$
$therefore L subscript 1 end subscript minus L subscript 2 end subscript equals 10 log invisible function application fraction numerator I subscript 1 end subscript over denominator I subscript 2 end subscript end fraction equals 10 log subscript 10 end subscript invisible function application left parenthesis 400 right parenthesis$
$rightwards double arrow L subscript 1 end subscript minus L subscript 2 end subscript equals 10 cross times 2.602 equals 26$
$L subscript 2 end subscript equals L subscript 1 end subscript minus 26 equals 80 minus 26 equals 54 blank d B$

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In a sonometer wire, the tension is maintained by suspending a 50.7 kg mass from the free end of the wire. The suspended mass has a volume of $0.0075 blank m to the power of 3 end exponent.$ The fundamental frequency of the wire is 260 Hz If the suspended mass is completely submerged in water, the fundamental frequency will become (take $g equals 10 blank m s to the power of negative 2 end exponent$ )

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