Answered

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 :

adelekeademolu

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

[tex]r_2 = r_1 \times 10^{\frac{|L_1-L_2|}{20}}[/tex]

where [tex]L_1[/tex] is the sound level at a distance of [tex]r_1[/tex] and

[tex]L_2[/tex] is the sound level at a distance of [tex]r_2[/tex].

Using the values in the question,

[tex]r_{2} = 25\times10^{\frac{|75-55|}{20}} \text{ m}[/tex]

[tex]r_2 = 25\times10^1 \text{ m}= 250 \text{ m}[/tex]

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

Other Questions