Answer:
The ratio is [tex]\frac{I_A}{I_B} = 3.6[/tex]
Explanation:
From the question we are told that
The position of the explosion from the ground is [tex]y = 78 \ m[/tex]
The distance of separation between the observers is [tex]d = 70 \ m[/tex]
Generally the intensity of sound varies inversely with the square distance from the source of the sound i.e
[tex]I = \frac{K}{d^2}[/tex]
Here k is a constant , so
[tex]I * d^2 = K[/tex]
=> [tex]I_A * d_A^2 = I_B * d_B ^2 = I_C * d_C^2[/tex]
Now given that observer A is directly under the explosion , the his distance from the sound is [tex]d_A = 78 \ m[/tex]
The distance of observer B from the explosion is [tex]d_B = 78 + 70 = 148 m[/tex]
while the distance of observer C from the explosion is [tex]d_C = 78 + 70 + 70 = 218 \ m[/tex]
Generally the ratio of the sound intensity heard by observer A to that heard by observer B is mathematically represented as
[tex]\frac{I_A}{I_B} = \frac{d_B^2}{d_A^2}[/tex]
=> [tex]\frac{I_A}{I_B} = \frac{148^2}{78^2}[/tex]
=> [tex]\frac{I_A}{I_B} = 3.6[/tex]
The ratio of the sound intensity heard by observer A to that heard by observer B will be [tex]I_A/I_B=[/tex] 3.6
The sound intensity or acoustic intensity is defined as the power carried out by the sound waves per unit area to the perpendicular direction to that area.
From the question, we have,
The position of the explosion from the ground is y=78 m
The distance of separation between the observers is d=70 m
Generally the intensity of sound varies inversely with the square distance from the source of the sound i.e
[tex]I=\dfrac{k}{d^2}[/tex]
Here k is a constant , so
[tex]I\times d^2=K[/tex]
[tex]I_A\times d_a^2=I_B\times d_B^2=I_C\times d_C^2[/tex]
Now given that observer A is directly under the explosion , the distance from the sound is [tex]d_A= 78\ m[/tex]
The distance of observer B from the explosion is [tex]d_B=78+70=148\ m[/tex]
while the distance of observer C from the explosion is [tex]d_C=78+70+70=218\ m[/tex]
Generally, the ratio of the sound intensity heard by observer A to that heard by observer B is mathematically represented as
[tex]\dfrac{I_A}{I_B} =\dfrac{d_B^2}{d_A^2}[/tex]
[tex]\dfrac{I_A}{I_B} =\dfrac{148^2}{78^2}[/tex]
[tex]\dfrac{I_A}{I_B} =3.6[/tex]
Thus the ratio of the sound intensity heard by observer A to that heard by observer B will be [tex]I_A/I_B=[/tex] 3.6
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