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

Answer:

250 m

Explanation:

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

Sound level (in decibels) is related to distance by

$r_2 = r_1 \times 10^{\frac{|L_1-L_2|}{20}}$

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,

$r_{2} = 25\times10^{\frac{|75-55|}{20}} \text{ m}$

$r_2 = 25\times10^1 \text{ m}= 250 \text{ m}$

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