Answer:
369.11 m
Explanation:
To solve this, we need first to write the expression to calculate the distance:
I1 * d1² = I2 * d2² (1)
Where:
I1 intensity of the sound at 261 m.
d1 distance of 261 m.
I2 intensity of the sound at d2 (Half of I1)
d2 distance required.
Now we know that I2 = 1/2I1, so replacing in (1) we have:
I1 * d1² = 1/2I1 * d2²
Solving now for d2:
2 * I1 * d1² / I1 = d2² ---> From here, I1 gets canceled so:
d2² = 2di²
Replacing the values of d1:
d2² = 2 * 261²
d2 = √136,242
d2 = 369.11 m
Answer:
d2 = 369.11 m
Explanation:
[tex]i_{1}[/tex] intensity of the sound at 261 m.
d1 distance of 261 m from te explosion
[tex]i_{2}[/tex] intensity of the sound at d2 ([tex]i_{1}[/tex])/2
d2 new distance
from te question,
we understand that I2 =([tex]i_{1}[/tex])/2 , so replacing in (1) we have:
[tex]i_{1}[/tex] * d1² =([tex]i_{1}[/tex])/2* d2²
d2:
2 *[tex]i_{1}[/tex] * d1² / I1 = d2² ---> From here, [tex]i_{1}[/tex] can be striked out
d2² = 2di²
substituting the values of d1:
d2² = 2 * 261²
d2 = √136,242
d2 = 369.11 m
