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

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

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=(k)/(15)\\\\k = 1425\ db.ft`

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

`L=\frac kd`

`L= (1425\ db.ft)/(48\ ft) = 29.688\ db`

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