Suppose that a single guitar player makes noise at 70 dB. If two guitar players play at the same time, the noise level will be approximately 73 dB. How many guitar players will it take for the sound intensity level to be 100 dB

it will take 1000 guitar players for sound intensity level to be 100 dB

Explanation:

Given that;

noise level of a single player = 70 dB

Intensity of one guitar will be;

SL= 10 × log(I/I₀)

where I₀ is hum threshold intensity = 10⁻¹² W/m²

I is intensity of sound produced by 1 guitar

SL is intensity level of one guitar

so we substitute

70 = 10 × log(I/10⁻¹²)

70/10 = log (I/10⁻¹²)

I = 10⁻¹² × 10⁷

I = 10⁻⁵ W/m²  

now Suppose n guitars produce sound intensity of 100 dB, then intensity of n guitars (In) will be;

100 = 10 × log(In/10⁻¹²)

log(In/10⁻¹²)  = 100/10

In = 10⁻¹² × 10¹⁰ =  10⁻² Wm²

we know that Now intensity of 1 guitar I = 10⁻⁵ W/m²

so Intensity of n guitars will be;

n × I = In

n = In / I

we substitute

n = 10⁻² Wm² /  10⁻⁵ W/m²

n = 1000

Therefore, it will take 1000 guitar players for sound intensity level to be 100 dB

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