Question

The sound intensity level from one solo flute is 70 dB. If 10 flutists standing close together play in unison, what will the sound intensity level be?

Answer 1

Answer:

80 dB

Explanation:

$I_0$ = Threshold intensity = $10^{-12}\ W/m^2$

I = Intensity of sound

$\beta$ = Intensity level of sound = 70 dB

Intensity level of sound is given by

$\beta=10log\dfrac{I}{I_0}\\\Rightarrow 70=10log\dfrac{I}{I_0}\\\Rightarrow \dfrac{70}{10}=log\dfrac{I}{10^{-12}}\\\Rightarrow 10^{\dfrac{70}{10}}=\dfrac{I}{10^{-12}}\\\Rightarrow \dfrac{I}{10^{-12}}=10^{\dfrac{70}{10}}\\\Rightarrow I=10^{7}\times 10^{-12}\\\Rightarrow I=10^{-5}\ W/m^2$

If there are 10 flutes $I=10\times 10^{-5}\ W/m^2$

$\beta=10log\dfrac{10\times 10^{-5}}{10^{-12}}\\\Rightarrow \beta=10log10^8\\\Rightarrow \beta=10\times 8\\\Rightarrow \beta=80\ dB$

The sound intensity level is 80 dB