The sound level produced by one singer is 63.4 dB. What would be the sound level produced by a chorus of 41 such singers (all singing at the same intensity at approximately the same distance as the original singer)? Answer in units of dB.
The sound level produced by one singer is 63.4 dB. What would be the sound level produced by a chorus of 41 such singers (all singing at the same intensity at approximately the same distance as the original singer)? Answer in units of dB.
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The sound level of 41 singers is approximately 79.52 dB.
Explanation:
As the sound level is given as 63.4 dB
The Intensity to Sound level relation is given as
[tex]\beta=10 log \dfrac{I}{I_o}\\[/tex]
Here β is given as 63.4 dB
I is to be calculated for 1 singer
I_o is constant as 10⁻¹²
So the equation is given as
[tex]\beta=10 log \dfrac{I}{I_o}\\I=10^{\beta/10}I_o\\I=10^{63.4/10}10^{-12}\\I=2.19 \times 10^{-4}[/tex]
Now as there are 41 singers so their I is given as
[tex]I_4_1=41*2.19 \times 10^{-4}\\I_4_1=0.0089[/tex]
Now the value of sound level is given as
[tex]\beta_4_1=10 log \dfrac{I_4_1}{I_o}\\\beta_4_1=10 log \dfrac{0.0089}{10^{-12}}\\\beta_4_1=79.52 dB[/tex]
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