Respuesta :
Given that,
Distance = 20.0 m
Average whisper = 20.0 dB
Sound level = 70.0 dB
We know that,
The minimum intensity is
[tex]I_{o}=10^{-12}\ W/m^2[/tex]
We need to calculate the sound intensity in the distance of 20 m
Using formula of sound intensity
[tex]dB=10\log(\dfrac{I_{a}}{I_{o}})[/tex]
Put the value into the formula
[tex]20=10\log(\dfrac{I_{a}}{10^{-12}})[/tex]
[tex]10^{2}=\dfrac{I_{a}}{10^{-12}}[/tex]
[tex]I_{a}=10^{-10}\ W/m^2[/tex]
If the conversation a sound level of 70.0 dB instead
We need to calculate the sound intensity
Using formula of sound intensity
[tex]dB=10\log(\dfrac{I_{b}}{I_{o}})[/tex]
Put the value into the formula
[tex]70=10\log(\dfrac{I_{a}}{10^{-12}})[/tex]
[tex]10^{7}=\dfrac{I_{b}}{10^{-12}}[/tex]
[tex]I_{b}=10^{-5}\ W/m^2[/tex]
We know that,
The intensity is inversely proportional with the square of the distance.
We need to calculate the distance
Using formula of intensity
[tex]\dfrac{I_{a}}{I_{b}}=\dfrac{R_{b}^2}{R_{a}^2}[/tex]
Put the value into the formula
[tex]\dfrac{10^{-10}}{10^{-5}}=\dfrac{R_{b}^2}{20^2}[/tex]
[tex]R_{b}^2=20^2\times\dfrac{10^{-10}}{10^{-5}}[/tex]
[tex]R_{b}=\sqrt{20^2\times\dfrac{10^{-10}}{10^{-5}}}[/tex]
[tex]R_{b}=0.063\ m[/tex]
Hence, The distance from the conversation should be 0.063 m.
The distance you should move to achieve a loudness of 70 dB is; 0.0633 m
We are given;
Average distance 1; R_1 = 20 m
Average whisper 1; dB1 = 20 dB
Average whisper 2; dB2 = 70 dB
Now, the formula for loudness in dB is;
dB = 10log(I/I_o)
Where;
I is the intensity of the sound
I_o is the minimum intensity that a human ear can detect = 10^(-12) W/m²
- Thus, for dB1 = 20 dB;
20 = 10log (I/10^(-12))
20/10 = log (I/10^(-12))
log (I/10^(-12)) = 2
10² = (I/10^(-12))
I = 10² × 10^(-12)
I_1 = 10^(-10) W/m²
- Similarly, for dB2 = 70 dB;
70 = 10log (I/10^(-12))
70/10 = log (I/10^(-12))
log (I/10^(-12)) = 7
10^(7) = (I/10^(-12))
I = 10^(7) × 10^(-12)
I_2 = 10^(-5) W/m²
The relationship between their intensities and distance is;
I_1/I_2 = (R_2/R_1)²
Where R_2 is the distance you should move to achieve a loudness of 70 dB.
Thus;
(10^(-10))/(10^(-5)) = R_2/20
(R_2)/20 = √(10^(-5))
(R_2)/20 = 0.00316227766
R_2 = 20 × 0.00316227766
R_2 = 0.0632 m
Read more at; https://brainly.com/question/21195959
