Question

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.

Answer 1

Answer:

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

$\beta=10 log \dfrac{I}{I_o}$

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

$\beta=10 log \dfrac{I}{I_o}\\I=10^{\beta/10}I_o\\I=10^{63.4/10}10^{-12}\\I=2.19 \times 10^{-4}$

Now as there are 41 singers so their I is given as

$I_4_1=41*2.19 \times 10^{-4}\\I_4_1=0.0089$

Now the value of sound level is given as

$\beta_4_1=10 log \dfrac{I_4_1}{I_o}\\\beta_4_1=10 log \dfrac{0.0089}{10^{-12}}\\\beta_4_1=79.52 dB$