The intensity of a certain sound wave is 6 μW/cm2. If its intensity is raised by 10 db, the new intensity (in μW/ cm2) is:
Select one:
a. 60
b. 600
c. 6.06
d. 6.6
a
A
To find the new intensity, we can use the formula for the relationship between intensity and decibels:
dB = 10 * log10(I / I0)
where dB is the increase in decibels, I is the new intensity, and I0 is the initial intensity.
Given that the initial intensity is 6 μW/cm2 and the increase in decibels is 10 dB, we can rearrange the formula to solve for I:
10 = 10 * log10(I / 6)
1 = log10(I / 6)
10^1 = I / 6
10 = I / 6
I = 6 * 10
I = 60
Therefore, the new intensity is 60 μW/cm2. Answer (a) is correct.
To find the new intensity of the sound wave, we need to understand the concept of decibels (dB) and how they relate to intensity.
The decibel scale is a logarithmic scale used to compare the intensity of sound waves or other types of waves. The formula to calculate the change in intensity in decibels (dB) is:
ΔdB = 10 * log10(I2/I1),
where ΔdB is the change in intensity in decibels, I1 is the initial intensity, and I2 is the final intensity.
In this case, the initial intensity is 6 μW/cm2, and we need to calculate the change in intensity in decibels. The change in intensity in decibels (ΔdB) is given as 10 dB.
So, we can rearrange the formula to solve for the final intensity (I2):
10 = 10 * log10(I2/I1).
Dividing both sides by 10, we get:
1 = log10(I2/I1).
Taking the inverse logarithm (base 10) of both sides, we have:
10^1 = I2/I1.
Simplifying further, we find:
10 = I2/I1.
Now, we substitute the initial intensity (I1 = 6 μW/cm2) into the equation:
10 = I2/6.
Multiplying both sides by 6, we get:
60 = I2.
Therefore, the new intensity (in μW/cm2) is 60.
So, the correct answer is a. 60.