Question

The sound level produced by one singer is 73.8 dB. What would be the sound level produced by a chorus of 35 such singers (all singing at the same intensity at approximately the same distance as the original singer)? Answer in units of dB.

Answer 1

89.241 dB.

Step-by-step explanation:

dB is the unit of sound intensity and it stands for the word 'decibels'. The sound intensity can be represented mathematically with the formula in the equation (1) below;

H = 10 log (b/b°). ---------------------------(1).

Note that the logarithm is in base 10. Also, the b° is known as the hearing threshold. The hearing threshold, b° has the unit of W/m^2 and it has the mathematically value of 10^-12.

So, in the question we are given that one singer A produces 73.8 dB. 35 singers singing at the same intensity will produce a sound level of;

H = 10 log [35b/ b°].

H = 10 log 35 + 10 log [b/b°].

Where 10 log [b/b°] = 73.8 dB that is to say the sound level produced by one singer. So, we will have;

H= 10 log 35 + 73.8 dB.

H= 89.2406804435027563 dB.

H= 89.241 dB.