Question

The intensity level of a "Super-Silent" power lawn mower at a distance of 1.0 m is 100 dB. You wake up one morning to find that four of your neighbors are all mowing their lawns using identical "Super-Silent" mowers. When they are each 20 m from your open bedroom window, what is the intensity level of the sound in your bedroom? You can neglect any absorption, reflection, or interference of the sound. The lowest detectable intensity is 1.0 × 10-12 W/m2.

Answer 1

Answer:

The intensity level in the room is 63 dB

Explanation:

To calculate the intensity of sound in the room, we use the equation of definition of decibels

     β = 10 log (I / Io)      (1)

With “I” the sound intensity and “Io” the threshold intensity 1.0 10⁻⁻¹² W/m²

To calculate the intensity we will use the initial data and remember the power of the emitted sound is constant, in addition that the sound propagates in three-dimensional form or on a spherical surface

      I = P/A    ⇒    P = I A

The area of ​​a sphere is 4 π r², where I can calculate of 1

     β/10 = log (I/Io)

   I / Io = ${10}^{\beta /10}$

   I = Io  ${10}^{\beta /10}$

   I = 1 10⁻¹² 10⁽¹⁰⁰/¹⁰⁾   = 1 10⁻¹² 10¹⁰

   I = 1.0 10⁻² W

With this we can calculate the intensity for a distance of 20 m

 I  = 1.0 10⁻² / ( 4π 20²)

 I =  2.0 10⁻⁶ W/m²

We have already found the intensity at the point of interest, so we can calculate the intensity in decibels at this point with equation 1

    β = 10 log(2.0 10⁻⁶ / 1.0 10⁻¹²)

    β = 10 log ( 2 10⁶) = 10  6.3

    β = 63 dB

The intensity level in the room is 63 dB