# Calculating Total Sound Intensity and Combined Sound Level: Ice Show Example"

• RedPhoenix
In summary, the conversation discusses a family ice show held at an enclosed arena where the skaters perform to music at a level of 80.0 dB. However, this is too loud for a baby who yells at 75.0 dB. The question is then posed about the total sound intensity and combined sound level. The solution involves converting the decibel values back to sound intensity using the equation dB = 10log(I/1E-12). The final answers are 1.316E-4 for the total sound intensity and 81.19 dBA for the combined sound level.
RedPhoenix

## Homework Statement

A family ice show is held at an enclosed arena. The skaters perform to music with level 80.0 dB. This is too loud for your baby, who yells at 75.0 dB.

(a) What total sound intensity engulfs you?
(b) What is the combined sound level?

## Homework Equations

dB = 10log(I/1E-12)

## The Attempt at a Solution

I am trying to convert back, but I have never been great with logs, and I cannot figure out how to get I.

80=10log(I/1E-12)
75=10log(I/1E-12)

EDIT - it just clicked - anti-derivatives
A)
75db = 10^7.5/1E12 = I(b)
80db = 10^8/1E12 = I(m)
add them for total = 1.316E-4

B)
10log(1.316E-4/1E-12)
81.19dB

Last edited:
A hint: Use the fact that 10^log x = x

To calculate the total sound intensity, we can use the equation dB = 10log(I/1E-12), where dB is the decibel level and I is the sound intensity in watts per square meter. By converting the decibel levels given in the problem to their corresponding sound intensities, we can add them together to find the total sound intensity. In this case, the sound intensity engulfing you would be 1.316E-4 W/m^2.

To calculate the combined sound level, we can use the same equation and convert the total sound intensity back to decibels. This can be done by taking the logarithm of the total sound intensity and multiplying it by 10. In this case, the combined sound level would be 81.19 dB. This indicates that the overall sound level is louder than either the music or the baby's yelling alone. It is important to consider the combined sound level in situations like this to ensure that the sound does not reach harmful levels.

## 1. How do I add decibels (dB) together?

To add dB, you must use logarithms to convert them into a linear scale. In other words, you must find the antilog of the dB values, add them together, and then take the logarithm of the sum to find the final dB value.

## 2. What is the formula for adding dB?

The formula for adding dB is: dBtotal = 10*log10(10dB1/10 + 10dB2/10 + ... + 10dBn/10), where dB1, dB2, ... , dBn are the individual dB values.

## 3. Can I simply add dB values together without using logarithms?

No, you cannot simply add dB values together without using logarithms. This is because dB is a logarithmic scale, meaning that the values are not directly additive. Instead, they must be converted into a linear scale before they can be added together.

## 4. Why do I need to use logarithms to add dB?

You need to use logarithms to add dB because dB is a logarithmic scale that is based on powers of 10. Logarithms are used to compress large numbers into a more manageable scale, making it easier to work with and compare values.

## 5. Is there a simpler way to add dB values together?

Unfortunately, there is no simpler way to add dB values together. Using logarithms is the only accurate method for adding dB values because it accounts for the logarithmic scale and properly converts the values into a linear scale before adding them together.

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