Question

A family ice show is held at an enclosed arena. The skaters perform to music with level 75.0 dB. This level is too loud for your baby, who yells at 70.0 dB (a) What total sound intensity engulfs you? W/m^2 (b) What is the combined sound level? dB

Answer 1

Answer:

(a). The total sound intensity $4.16\times10^{-5}$.

(b). The combined sound level 76.19 dB.

Explanation:

Given that,

Sound level = 75.0 dB

We need to calculate the noise

Using formula of intensity

$I=I_{0}\ 10^{\frac{\beta}{10}}$

Put the value into the formula

$I_{n}=10^{-12}\times10^{\dfrac{75.0}{10}}$

$I_{n}=0.0000316= 3.16\times10^{-5}$

We need to calculate the sound intensity

$I_{s}=10^{-12}\times10^{\dfrac{70.0}{10}}$

$I_{s}=0.00001=1.0\times10^{-5}$

(a). We need to calculate the total sound intensity

The total sound intensity

$I=I_{n}+I_{s}$

$I=3.16\times10^{-5}+1.0\times10^{-5}$

$I=4.16\times10^{-5}\ dB$

(b). We need to calculate the combined sound level

Using formula of sound level

$sound\ level =10 log(\dfrac{I}{I_{0}})$

$sound\ level =10 log(\dfrac{4.16\times10^{-5}}{10^{-12}})$

$sound\ level=76.19\ dB$

Hence, (a). The total sound intensity $4.16\times10^{-5}$.

(b). The combined sound level 76.19 dB.