A tiny source emits sound uniformly in all directions. The intensity level ar a dist. Of 2m is 100dB. How much sound power is the soure emitting?

You didn’t calculate the power you calculated the intensity . To calculate power use I=Power/4pieR^2

To calculate the sound power emitted by the source, we can use the relationship between intensity level and sound power.

The formula to calculate intensity level (IL) in decibels (dB) is given by:

IL = 10 * log10(I/I0)

Where I represents the intensity of the sound wave and I0 is the reference intensity level.

In this case, the intensity level (IL) is 100 dB and the distance (r) is 2 m.

We need to convert the intensity level to intensity:

IL = 10 * log10(I/I0)
100 = 10 * log10(I/I0)

First, we need to find the reference intensity (I0) level. The reference intensity (Io) is the threshold of hearing and is equal to 10^-12 Watts per square meter (W/m^2).

Substituting the values:

10 * log10(I/I0) = 100
log10(I/I0) = 10
I/I0 = 10^10

Next, we can rearrange the equation to solve for the intensity (I):

I = (I0) * (10^10)
I = (10^-12) * (10^10)
I = 10^-12+10
I = 10^-2

Finally, we can calculate the sound power (P) emitted by the source using the formula:

P = I * A

Where P is the sound power, I is the intensity, and A is the area of a sphere with a radius of 2 m.

The area of a sphere is given by:

A = 4 * π * r^2

Substituting the values:

A = 4 * π * (2^2)
A = 4 * π * 4
A = 16 * π

Now, we can calculate the sound power:

P = (10^-2) * (16 * π)
P = 16π * 10^-2
P ≈ 0.50265 Watts

Therefore, the source is emitting approximately 0.50265 Watts of sound power.

To find out how much sound power the source is emitting, we need to make use of the formula that relates intensity level and sound power. Intensity level is measured in decibels (dB), while sound power is measured in watts (W).

The formula to calculate intensity level (L) in terms of sound power (P) and reference intensity (I₀) is:

L = 10 * log₁₀(I / I₀)

Where I is the sound intensity. In our case, the intensity level (L) is given as 100 dB.

Given that the distance from the source to the measuring point is 2 m, we need to find the sound intensity (I) to determine the sound power (P).

The formula to calculate sound intensity (I) for a point source is:

I = P / (4πr²)

Where P is the sound power emitted by the source, and r is the distance from the source to the measuring point.

Substituting the known values into the equation, we have:

100 = 10 * log₁₀(P / (4π(2)²))

Simplifying further:

10 = log₁₀(P / (16π))

Now, we need to solve for P to find the sound power emitted by the source.

To do that, we will first convert the equation into exponential form:

10¹⁰ = (P / (16π))

Next, isolate P:

P = 10¹⁰ * 16π

P ≈ 5.03 * 10¹²π

Therefore, the sound power emitted by the source is approximately 5.03 * 10¹²π watts.

db = 10*Log W/Wo = 100

10*Log W/10^-12 = 100
Log W/10^-12 = 10
Log W - Log 10^-12 = 10
Log W = 10 + Log 10^-12 = 10-12 = -2
W = 10^-2 = 0.01 Watts.