The loudness,
L
L, of a sound (measured in decibels, dB) is inversely proportional to the square of the distance,
d
d, from the source of the sound. Round to 3 decimal places.
A person 15 feet from a jetski, it is 75 decibels loud.
How loud is the jetski when the person is 47 feet away?
Well, let's use some clown humor to calculate that, shall we?
If a jetski is like a rock star and the person is its fan, we can say that the fan's enthusiasm for the sound decreases as the distance increases. It's like the fan getting further away from the rock star at a concert.
So, using the inverse square relationship, we can calculate the loudness of the jetski when the person is 47 feet away:
(75 dB) × ((15 ft)² / (47 ft)²) ≈ 29.129 dB
So, when the person is 47 feet away from the jetski, it will be approximately 29.129 decibels loud. Rock on, but not too loudly!
To find the loudness of the jetski when the person is 47 feet away, we can use the inverse square relationship.
Let's assume the loudness of the jetski at 15 feet is L1 and the loudness at 47 feet is L2.
According to the inverse square relationship:
L1 / L2 = (d2^2) / (d1^2)
where d1 is the distance from the jetski at which the loudness is L1, and d2 is the distance from the jetski at which the loudness is L2.
Plugging in the given values:
L1 / L2 = (47^2) / (15^2)
Simplifying further:
L1 / L2 = 2209 / 225
Now, we can solve for L2 (loudness at 47 feet):
L2 = L1 * (225 / 2209)
Given that the loudness at 15 feet is 75 decibels, we substitute L1 = 75:
L2 = 75 * (225 / 2209)
Calculating:
L2 ≈ 76.532 dB
Therefore, the jetski would be approximately 76.532 decibels loud when the person is 47 feet away.
To solve this problem, we can use the formula for inverse variation:
L = k/d^2
where L represents the loudness, d represents the distance, and k is a constant.
First, we can find the value of k using the given information that when the person is 15 feet away, the loudness is 75 decibels:
75 = k/(15^2)
75 = k/225
To find k, we can multiply both sides of the equation by 225:
75 * 225 = k
k = 16875
Now that we have the value of k, we can use it to find the loudness when the person is 47 feet away:
L = 16875/(47^2)
L = 16875/2209
L ≈ 7.64 decibels
Therefore, when the person is 47 feet away from the jetski, it is approximately 7.64 decibels loud.
L = k(1/d^2)
for the given:
75 = k(1/225)
k = 16875
L = 16875/d^2
then if d = 47
L = 16875/47^2 = 7.6 decibels