# Help calculating decibel level from intensity of sound

• RichardGib
In summary, to determine the decibel rating of a sound with an intensity of 1.0 x 10-5 W/m2, the equation dB = 10 * log( I / 1.0 x 10-12 W/m2) can be used. By plugging in the given values, the decibel rating is found to be 70dB. Similarly, for a sound with an intensity of 6.1 x 10-6 W/m2, the decibel rating would be 68dB.
RichardGib

## Homework Statement

Determine the decibel rating of the following intensities of sound.

I = 1.0 x 10-5 W/m2

## Homework Equations

The equation which relates the intensity of a sound wave to its decibel level is:

dB = 10 * log( I / 1.0 x 10-12 W/m2)

## The Attempt at a Solution

dB = 10 * log( 1 x 10-5 W/m2 / 1.0 x 10-12 W/m2) = ?

I put it into my calculator and can't actually get an answer out of it. I know the answer is 70dB as I looked in the answer booklet but I couldn't get that answer by entering the equation into it?

Any help would be greatly appreciated. Thanks

It's right there, 10(12 - 5)=70 by inspection.

Doug Huffman said:
It's right there, 10(12 - 5)=70 by inspection.
Thankyou. How would this one be worked out? I am very new to physics so equations are confusing at the moment:

dB = 10 * log( 6.1 x 10-6 W/m2 / 1.0 x 10-12 W/m2) = 68 dB

How would that be inputted into a calculator?

Thank you very much :)

LOL Sorry, I haven't used a calculator in many years.

My collection of calculators (HP-35, 41, 48) live in the same box with a half-dozen slide rules.

Doug Huffman said:
LOL Sorry, I haven't used a calculator in many years.
No worries. Thank you for your help!

## What is the relationship between intensity and decibel level of sound?

The decibel (dB) is a unit used to measure the level of sound intensity. It is a logarithmic scale, meaning that a small change in intensity corresponds to a large change in decibel level. The formula for calculating decibel level from intensity is: dB = 10 log(I/I0) where I is the sound intensity and I0 is the reference intensity (usually 10-12 watts per square meter).

## How does the decibel level of sound affect human hearing?

The decibel scale is logarithmic because the human ear perceives sound in a similar way. A change of 10 dB represents a perceived doubling or halving of loudness. A change of 20 dB is perceived as four times louder or quieter. Exposure to sounds above 85 dB can cause hearing damage, and prolonged exposure to sounds above 120 dB can cause immediate damage.

## Can decibel level be converted to other units of measurement?

Yes, decibels can be converted to other units such as sound pressure level (SPL) in pascals or sound power level (SWL) in watts. This can be done using different conversion factors depending on the type of measurement being used.

## What is the practical use of calculating decibel level from intensity of sound?

Calculating decibel levels from intensity is important in many fields such as acoustics, audiology, and noise control. It helps in measuring and controlling sound levels in different environments, determining the effects of noise on humans and animals, and evaluating the effectiveness of hearing protection devices.

## How accurate are decibel level measurements?

Decibel level measurements can vary depending on the instrument used and the method of measurement. It is important to calibrate instruments regularly and follow proper measurement procedures to ensure accuracy. It is also important to note that decibel levels can be affected by factors such as distance, direction, and frequency of the sound.

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