# How Does a 2.80 dB Difference Affect Sound Intensity?

• Oijl
In summary, the equation B = 10dB log(I/Io) can be used to find the ratio of intensities between two sounds, given the difference in their sound levels. By taking the difference in sound levels and using the laws of logarithm, the ratio of intensities can be found.
Oijl

## Homework Statement

Two sounds differ in sound level by 2.80 dB. By what factor is the one intensity greater than the other?

## The Attempt at a Solution

Is the equation

$$B$$ = 10dB log(I/Io)

relevant?

The equation is
Bdb = 10log(I/Io)
Now let B1 = 10log(I1/Io) and
B2 = 10log(I2/Io)
Take the difference and find the ratio of I1/I2.

Lets say sound 1 has an intensity of I1 and intensity level B, and sound 2 has an intensity of I2 with intensity level B+2.8

B = 10 log (I1 / I0)
B+2.8 = 10 log (I2 / I0)

See if you can use those

EDIT: rl.bhat beat me to it :P

I'm sorry, but the algebra is confusing me. Could you show the first few steps, please?

B1 = 10log(I1/Io)
B2 = 10log(I2/Io)
B1 -B2 = 10[log(I1/Io) - log(I2/Io)]
Use laws of logarithm to further simplification.

## 1. What is DB difference?

DB difference is a measure of the difference in decibels between two sound levels. It is used to quantify the change in sound intensity or loudness.

## 2. How is DB difference calculated?

DB difference is calculated by taking the logarithm of the ratio of the two sound levels. The formula is DB difference = 10 log (sound level 1 / sound level 2).

## 3. What is the significance of DB difference in sound measurement?

DB difference is important because it allows us to compare and quantify the difference in sound levels. It is commonly used in noise pollution measurements and in audio engineering to adjust sound levels.

## 4. Can DB difference be negative?

Yes, DB difference can be negative. This means that the second sound level is higher than the first sound level, resulting in a negative value. A negative DB difference indicates a decrease in sound intensity.

## 5. Is DB difference the same as DB intensity?

No, DB difference and DB intensity are not the same. DB intensity is a measure of the absolute sound intensity, while DB difference is a measure of the change in sound intensity between two levels. DB intensity is measured in decibels, while DB difference is a unitless value.

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