The sound level produced by one singer is 70.8 dB. What would be the sound level produced by a chorus of 37 such singers (all singing at the same intensity at approximately the same distance as the original singer)

86.48 dB

Explanation:

86.48 dB

Explanation:

sound level intensity, β = 70.8 dB

Io = 10^-12 W/m²

Let the intensity if I at the level of 70.8 dB

Use the formula

7.08 = log I + 12

log I = - 4.92

I = 1.2 x 10^-5 W/m²

There are 37 singers, so the total intensity is I'.

I' = 37 x I

I' = 37 x 1.2 x 10^-5 = 4.45 x 10^-4 W/m²

Let the sound intensity is β' in decibels.

Use the formula

β' = 86.48 dB

86.48 dB. Ans

Explanation:

Sound level by one singer = 70.8 dB

= 7.08 B

If I be its intensity in terms of watt/m²

log (I / 10⁻¹²) = 7.08 (given)

I / 10⁻¹² = 10⁷°⁰⁸

I = 10⁻¹² x 10⁷°⁰⁸

= 10⁻⁴°⁹²

=.000012022 W / m²

intensity by 37 singers

= 37 x. 000012022 W / m²

=.0004448378

= 4448.378 x 10⁻⁷

intensity level

= log I / 10⁻¹² B

= log 4448.378 x 10⁻⁷ / 10⁻¹²

= log 444837800 B

log 4448378 + 2 B

= 6.6482 + 2 B

8.6482 B

intensity level = 8.6482 B

= 86.48 dB. Ans