A listener moves from a distance of 120 inches to 300 inches from a loudspeaker. What is the expected change in decibels?

To understand the expected change in decibels when a listener moves away from a loudspeaker, it's important to remember that sound intensity diminishes as the distance from the source increases. The relationship between distance and sound level can be calculated using the inverse square law, which states that sound intensity decreases proportionally to the square of the distance from the source.

In this case, the listener moves from a distance of 120 inches to 300 inches. To calculate the change in decibels, we can use the formula:

[

\Delta dB = 20 \cdot \log_{10}\left(\frac{D_1}{D_2}\right)

]

where (D_1) is the initial distance and (D_2) is the final distance. Plugging in the values:

• (D_1 = 120) inches

• (D_2 = 300) inches

Calculating the ratio of the distances:

[

\frac{D_1}{D_2} = \frac{120}{300} = 0.4

]

Now, calculating the logarithm:

[

\Delta dB = 20 \cdot \log_{10