The sound level at a point is increased by 30dB. by what factor is the pressure amplitude increased?? ¿¿
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As We know that the sound level at a point is increased by 30 dB.
Sound level in dB will be β = 10 log₁₀[I/I₀].
If I₁ and I₂ are the intensities and β₁ and β₂ are the sound levels in the two cases.
→ β₂ – β₁ = 10[log₁₀(I₂/I₀) – log₁₀(I₁/I₀)]
→ 30 = 10 log₁₀(I₂/I₁)
→ 3 = log₁₀(I₂/I₁)
→ I₂/I₁ = 10³
As We also know that the Intensity is ∝ to the square of the pressure amplitude.
→ [P₂/P₁]² = I₂/I₁
→ [P₂/P₁]² = 10³
→ P₂/P₁ = √1000
→ P₂/P₁ ≈ 32
Hence,
The pressure amplitude increased by 32 (approx.).
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