How many nanoseconds does it take light to travel 1.00 ft in vacuum? (This result is a useful quantity to remember.)
1 answer:
To solve this problem, we will define speed as the amount of distance traveled per unit of time. We will clear the value of time and in parallel we will convert the Units to an international system to facilitate the calculation since we know the speed of light in a vacuum. The speed defined in terms of distance and time would be
The speed of light in a vacuum is and 1ft is equivalent to
, so the estimated time would be
We know that 1 second is equivalent to , therefore
Therefore the time is 1.02ns
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Answer:
r₂ = 0.316 m
Explanation:
The sound level is expressed in decibels, therefore let's find the intensity for the new location
β = 10 log
let's write this expression for our case
β₁ = 10 log \frac{I_1}{I_o}
β₂ = 10 log \frac{I_2}{I_o}
β₂ -β₁ = 10 ( )
β₂ - β₁ = 10
log \frac{I_2}{I_1} = = 3
= 10³
I₂ = 10³ I₁
having the relationship between the intensities, we can use the definition of intensity which is the power per unit area
I = P / A
P = I A
the area is of a sphere
A = 4π r²
the power of the sound does not change, so we can write it for the two points
P = I₁ A₁ = I₂ A₂
I₁ r₁² = I₂ r₂²
we substitute the ratio of intensities
I₁ r₁² = (10³ I₁ ) r₂²
r₁² = 10³ r₂²
r₂ = r₁ / √10³
we calculate
r₂ =
r₂ = 0.316 m