Question

A person standing a certain distance from four identical loudspeakers is hearing a sound level intensity of 125 dB. What sound level intensity would this person hear if all but one are turned off?

Answer 1

The sound level intensity would be 10 * log(1/3)dB.

Step-by-step explanation:

To determine the sound level intensity that a person would hear if all but one of the identical loudspeakers are turned off, we need to consider the relationship between intensity and sound level in decibels (dB).

The sound level intensity is measured on a logarithmic scale, so we can use the formula:

Sound level (dB) = 10 * log (intensity ratio)

Since all the loudspeakers are identical, turning off three of them means reducing the intensity of the sound by a factor of 3.

Therefore, the new sound level intensity would be:

Sound level (dB) = 10 * log (1/3)

Answer 2

`\mathbf{\beta = 123.75 \ dB}`

Step-by-step explanation:

From the question, using the expression:

`125 \ dB = 10 \ log ((I)/(I_o))`

where;

`I_o = 10^(-12) \ W/m^2`

`I = 10^(12.5) * 10^(-12) \ W/m^2`

`I = 3.162 \ W/m^2`

This is a combined intensity of 4 speakers.

Thus, the intensity of 3 speakers =
`(3.162* 3)/(4)`

= 2.372 W/m²

Thus;

`\beta = 10 \ log ( (2.372)/(10^(-12)) ) \ W/m^2`

`\mathbf{\beta = 123.75 \ dB}`