If a listener moves from 156 inches to 276 inches away from a loudspeaker, what is the expected change in decibels?

To find the change in decibels when a listener moves away from a loudspeaker, we use the principle that sound intensity decreases with distance. Specifically, sound intensity decreases by 6 dB for every doubling of distance from the source in free-field conditions.

First, calculate the ratio of the distances:

1. Initial distance: 156 inches

2. New distance: 276 inches

Now, we compare these distances. The factor by which the distance has increased can be calculated as follows:

[

\text{Distance factor} = \frac{\text{New distance}}{\text{Initial distance}} = \frac{276}{156} \approx 1.769

]

To find out how many doubles are in this distance factor, we need to estimate how many times 156 inches would double before reaching 276 inches:

• The first double of 156 inches is 312 inches (which exceeds 276), thus we have only one doubling factor that falls short.

Since one complete doubling corresponds to a decrease of 6 dB, we can approximate the reduction in decibels for the factor of 1.769 as follows:

To find the decrease in dB, we will apply the logarithmic scale of sound