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

To solve both parts, convert the decibel levels into intensities, sum them to find the total intensity, and then recalculate the decibel level for the combined intensity using logarithms.

Step-by-step explanation:

The question involves calculating the total sound intensity and the combined sound level when two sounds of different decibels are present.

Part (a) - Total Sound Intensity

To find the total sound intensity that engulfs you, you first need to convert the decibel levels to intensities using the formula:

I = I0 × 10ß/10

where I is the intensity in watts per square meter (W/m2), I0 is the threshold intensity (10-12 W/m2), and ß is the decibel level.

Next, add the intensities together to get the total sound intensity.

Part (b) - Combined Sound Level

The combined sound level is not simply the sum of the two decibel levels; instead, it is calculated by taking the logarithm of the sum of the intensities. Use the formula:

ßtotal = 10 × log10(Itotal ÷ I0)

Apply this formula using the total intensity found in part (a) to calculate the combined sound level in decibels (dB).

Answer 2

(a). The total sound intensity
`4.16*10^(-5)`.

(b). The combined sound level 76.19 dB.

Step-by-step explanation:

Given that,

Sound level = 75.0 dB

We need to calculate the noise

Using formula of intensity

`I=I_(0)\ 10^{(\beta)/(10)}`

Put the value into the formula

`I_(n)=10^(-12)*10^{(75.0)/(10)}`

`I_(n)=0.0000316= 3.16*10^(-5)`

We need to calculate the sound intensity

`I_(s)=10^(-12)*10^{(70.0)/(10)}`

`I_(s)=0.00001=1.0*10^(-5)`

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

The total sound intensity

`I=I_(n)+I_(s)`

`I=3.16*10^(-5)+1.0*10^(-5)`

`I=4.16*10^(-5)\ dB`

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

Using formula of sound level

`sound\ level =10 log((I)/(I_(0)))`

`sound\ level =10 log((4.16*10^(-5))/(10^(-12)))`

`sound\ level=76.19\ dB`

Hence, (a). The total sound intensity
`4.16*10^(-5)`.

(b). The combined sound level 76.19 dB.