Question

The loudness, L, of a sound (measured in decibels, dB) is inversely proportional to the square of the distance, d, from the source of the sound. A person 15 feet from a jetski, it is 95 decibels loud. How loud is the jetski when a person is 48 feet away?

Answer 1

Answer:

Jet ski is 29.688 db Loud when a person is 48 feet away.

Step-by-step explanation:

Given:

$L$ ∝ $\frac1d$

Distance of a person from Jet ski = 15 feet

Loudness of the sound = 95 decibels

We need to find the Loudness when the distance of person is 48 feet away.

Solution:

$L$ ∝ $\frac1d$

so we get;

$L=\frac kd$

Where k ⇒ Constant.

first we will find value of k when $L=95\ db; d= 15\ ft$

Substituting the values we get;

$95=\frac{k}{15}\\\\k = 1425\ db.ft$

Now we need to find $L$ when $d =48\ ft$

$L=\frac kd$

$L= \frac{1425\ db.ft}{48\ ft} = 29.688\ db$

Hence Jet ski is 29.688 db Loud when a person is 48 feet away.