A skyrocket explodes 77 m above the ground. Three observers are spaced 106 m apart, with observer A directly under the point of the explosion. Find the ratio of the sound intensity heard by observer A to that heard by observer B.
Find the ratio of the intensity heard by observer A to that heard by observer C.
To find the ratio of the sound intensity heard by observer A to that heard by observer B and C, we can use the inverse square law of sound propagation.
The inverse square law states that the sound intensity decreases inversely proportional to the square of the distance from the source. Mathematically, it can be expressed as:
I ∝ 1/d^2
where I is the sound intensity and d is the distance from the source.
Let's calculate the distances of observer A, B, and C from the point of explosion:
Distance of observer A from the point of explosion = 0m (directly under the explosion)
Distance of observer B from the point of explosion = 106m (106m apart from observer A)
Distance of observer C from the point of explosion = 2*106m = 212m (twice the distance between observer A and B)
Now, let's calculate the ratio of the intensity heard by observer A to that heard by observer B and C:
Ratio of intensity A to B = (1/d_a^2) / (1/d_b^2) = d_b^2 / d_a^2
Substituting the values, we get:
Ratio of intensity A to B = (106m)^2 / (0m)^2 = 11236
The ratio of intensity heard by observer A to that heard by observer B is 11236.
Ratio of intensity A to C = (1/d_a^2) / (1/d_c^2) = d_c^2 / d_a^2
Substituting the values, we get:
Ratio of intensity A to C = (212m)^2 / (0m)^2 = ∞
The ratio of intensity heard by observer A to that heard by observer C is infinity since observer C is at an infinite distance from the explosion.
So, the final answers are:
- The ratio of intensity heard by observer A to that heard by observer B is 11236.
- The ratio of intensity heard by observer A to that heard by observer C is infinity.