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Paraphin [41]
3 years ago
9

The low-frequency speaker of a stereo set produces 10.0 W of acoustical power. If the speaker projects sound uniformly in all di

rections, at what distance from the speaker is the intensity level 80.0 dB
Physics
1 answer:
Paha777 [63]3 years ago
6 0

Answer:

the required distance is 89.125 m

Explanation:

Given the data in the question;

we know that, sound intensity B in decibels of sound is;

β(dB) = 10log₁₀( I / I_0 )

where intensity I = power / area carried by wave

I_0 = 10⁻¹² W/m² { minimum threshold intensity }

Now,

intensity I = power / area carried by wave = P/A = P/4πr² { spherical  }

given that; β = 80.0 dB and P = 10 W

so

β(dB) = 10log₁₀( I / I_0 )

we substitute

80 = 10log₁₀( P / 4πr²× I_0)

80 = 10log₁₀( 10 / 4πr²× 10⁻¹² )

8 = log₁₀(10) - log₁₀( 4πr²× 10⁻¹² )  

8 = 1 - log₁₀( 4πr²× 10⁻¹² )

8 - 1 = -log₁₀( 4πr²× 10⁻¹² )

7 = -log₁₀( 1.2566 × 10⁻¹¹ × r² )

7 = -[ log₁₀( 1.25 × 10⁻¹¹) + log₁₀( r² ) ]

7 = -[ -10.9 + log₁₀( r² ) ]

7 = 10.9 - log₁₀( r² )

-log₁₀( r² ) = 7 - 10.9

-log₁₀( r² )  = - 3.9

log₁₀( r² ) = 3.9

2log₁₀r = 3.9

log₁₀r  = 3.9 /2

log₁₀r = 1.95

r = 89.125 m

Therefore, the required distance is 89.125 m

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