Understanding dB: Explaining Intensity Level of Sound in a Factory

[stumped23]

'The intensity level of sound in a factory is 93.0 dB when all seven of its machines are working. If four machines are shut down for maintenance, what is the intensity level of the sound from the remaining machines? Assume that all seven machines are identical.'

I know the answer is not just 3/7*93 as dB are similar to the richter scale. I found http://en.wikipedia.org/wiki/Decibel" and am trying to apply the third formula under 'Defintion' but to little success. I'm very confused.

Could anyone explain a little clearer exactly what the dB is?

 

[HallsofIvy]

Reverse your formula: all 7 machines are 7/3 as loud as only 3 so you must have 93.0= 10log((7/3)X) where X is the intensity of 3 machines.

 

[kyle8921]

I can provide a clear explanation of what decibels (dB) are and how they relate to intensity level of sound. Decibels are a unit of measurement used to express the ratio between two values, typically in terms of power or intensity. In the case of sound, decibels are used to measure the intensity level of a sound wave, which is the amount of energy that the sound wave carries per unit area.

The decibel scale is logarithmic, meaning that an increase of 10 dB represents a tenfold increase in intensity level. This is why the answer of 3/7 * 93 dB is not correct - the intensity level does not decrease linearly with the number of machines.

To calculate the intensity level of the remaining machines, we can use the following formula:

IL1 = IL2 + 10log(N1/N2)

Where IL1 is the intensity level with all seven machines working, IL2 is the intensity level with four machines shut down, N1 is the number of machines with all seven working, and N2 is the number of machines with four shut down.

Plugging in the values given in the question, we get:

IL1 = 93 dB, IL2 = ?, N1 = 7, N2 = 3

IL2 = 93 + 10log(7/3)

IL2 = 93 + 10 * 0.477

IL2 = 93 + 4.77

IL2 = 97.77 dB

Therefore, the intensity level of the remaining machines is 97.77 dB when four machines are shut down for maintenance. This means that the sound intensity has increased by about four times, which is significant and may have implications for noise levels in the factory.

In conclusion, decibels are a unit of measurement used to express the intensity level of a sound wave. They are logarithmic in nature and a change of 10 dB represents a tenfold increase in intensity level. Using the formula provided, we can accurately calculate the intensity level of the remaining machines in the factory.