# Sound intensity level

#### Mooki

A sound wave is measured to have a 20-decibel sound intensity level (SIL). And the sound wave power flux (measured in Watts/m2) is then increased by a factor of 2000. What is the new sound level (in decibels) after this factor of 2000 increase in sound power?

I figured that 20 db = I
but what is this power flux increase? (2000) is it Io?

What formulas should i use to solve this?

Thank you.

#### werehk

PHF Hall of Fame
let me give you a hint.
Use
Sound intensity level= 10log(I/I_0)
I is the sound intensity which is proportional to the power
I_0 is the minimum sound intensity that can be heard

#### Mooki

10log(20 / 10-12W/m2) = 10log(20000000 MegaWatt) = 7.301

Don't think that's correct though.

One thing i do not understand is this factor increase by 2000.

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#### Mooki

20dB = 10log(I+2000/10-12W/m2)
20dB = 10log(2000 Wm-2 /10-12W m2)
20dB = 10log(2000 / 0.0000000000001W m2)
20dB = 10log(20000000000000000)
20dB = 12.529

is this correct?

#### werehk

PHF Hall of Fame
Let the sound intensity I with sound intensity level p, the new sound intensity level be x
p=10log(I/I_0)------------------------(1)
For the second equation,

x=10log(2000I/I_0)-------------------------(2)
x= 10log(I/I_0) + 10log2000
the above is by using log property

you will find that the sound
x=p+10log2000
so the sound intensity level is increased by 10log2000 dB

#### anwaar

echo means reflection of sound, simply use the speed formula, in this case the distance travelled is doubled.

werehk