# The intensity of a certain sound wave is 6 ì W.cm2. if its intensity is raised by 10 decibels, the new intensity (in ìW/cm2) is :

a. 60
b. 6.6
c. 6.06
d. 600
E. 12

You can calculate this if you wish using logs, but you can do it in your head: 3 db means double power, 6 db means 4x power, 9 db means 8x power, and ...10db means a power of 10x.

10db=10 log (P/6)
1= log (p/6)
10^1=P/6
p=60W/cm^2

You can calculate this if you wish using logs, but you can do it in your head: 3 db means double power, 6 db means 4x power, 9 db means 8x power, and ...10db means a power of 10x.

10db=10 log (P/6)
1= log (p/6)
10^1=P/6
p=60W/cm^2

## The new intensity of the sound wave, after raising it by 10 decibels, is 60 ì W.cm2 (option a).

Explanation:
To calculate the new intensity, we use the formula for decibels:

dB = 10 log(I/I0)

where I is the intensity of the new sound wave and I0 is the intensity of the original sound wave.

Given that the original intensity is 6 ì W.cm2, we can rewrite the formula as:

10 = 10 log(I/6)

Dividing every term by 10:

1 = log(I/6)

To isolate I, we can use the property of logarithms that states that 10 raised to the power of log(base10) of a number is equal to the number itself:

10^1 = I/6

Simplifying:

I = 10 * 6 = 60 ì W.cm2

Therefore, the new intensity is 60 ì W.cm2 (option a).