Sound the loudness of a sound l in decibels is defined by l= 10 log.r, where r is the relative intensity of the sound. a chofr director wants to determine how many members could sing while maintaining a safe level of sound, about 80 decibels. if one person has a relative intensity of 10 when singing, then how many people could sing with the same relative intensity to achieve a loudness of 80 decibels?

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tushargupta0691 tushargupta0691 · Answer 1 · 2022-07-24T04:09:47+02:00

Around 298 people can sing together with the same relative intensity to achieve a loudness of 80 decibels.

Given Information

Loudness of sound is given as, l = 10 log₁₀r

Here, r is the relative intensity.

Relative intensity of a single person when singing = 10

Loudness to be achieved, L = 10 decibels

Calculating the Number of People

Let the number of people with relative intensity 10 singing together be n decibels, then to produce a loudness of 80 decibels, we have,

80 = 10 log₁₀(r × n)

80 = 10 log₁₀(10 × n) [∵ r = 10]

log₁₀(10 × n) = 8

10n ≈ 2980

n = 298

Therefore, 298 people, each with a relative intensity of 10 decibels can sing together to achieve a loudness of 80 decibels.

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