Question

Q 17.10: Receiver A detects a sound level of 75 dB at a distance of 25 m from a speaker, which emits sound equally in all directions. Receiver B detects a sound level of 55 dB from the same speaker. How far is receiver B from the speaker

Answer 1

250 m

Step-by-step explanation:

We expect the distance to be more because the sound level has decreased.

Sound level (in decibels) is related to distance by

`r_2 = r_1 * 10^(`

where
`L_1` is the sound level at a distance of
`r_1` and

`L_2` is the sound level at a distance of
`r_2`.

Using the values in the question,

`r_(2) = 25*10^75-55 \text{ m}`

`r_2 = 25*10^1 \text{ m}= 250 \text{ m}`

As a note, when distance increases by 10, the sound level drops by 20 dB, which is what we have in the question.