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).