Question

A small omni directional source of noisy sound emits uniformly with a power of 40W.Determine the distance from the source for which the sound level is 90dB. Calculate also the intensity level at a point 100m from the source. (if there is no absorption)

Answer 1

Any one pls

Answer 2

[AI-generated answer — Step-by-Step Bot]

To determine the distance from the source for which the sound level is 90dB, we can use the formula for sound intensity level:

L = 10 * log10(I/I0)

where L represents the sound level in decibels (dB), I represents the sound intensity, and I0 is the reference intensity (usually taken as 10^-12 W/m^2).

Given that the power emitted by the source is 40W, we can calculate the sound intensity at a distance r from the source using the formula:

I = P / (4 * π * r^2)

where P is the power emitted by the source, r is the distance from the source, and π is a mathematical constant approximately equal to 3.14159.

Let's calculate the distance from the source for which the sound level is 90dB:

L = 90dB
I0 = 10^-12 W/m^2
P = 40W

We can rearrange the formula to solve for distance r:

L = 10 * log10(P / (4 * π * r^2)) + 10 * log10(1/I0)
90 = 10 * log10(40 / (4 * π * r^2)) + 10 * log10(1/10^-12)
90 = 10 * log10(40 / (4 * π * r^2)) + 10 * log10(10^12)
90 - 10 * log10(10^12) = 10 * log10(40 / (4 * π * r^2))
90 - 120 = 10 * log10(40 / (4 * π * r^2))
-30 = 10 * log10(40 / (4 * π * r^2))
-3 = log10(40 / (4 * π * r^2))
10^-3 = 40 / (4 * π * r^2)
10^-3 = 10 / (π * r^2)
r^2 = 10 / (π * 10^-3)
r = sqrt(10 / (π * 10^-3))
r ≈ 1.78 meters

Therefore, the distance from the source for which the sound level is 90dB is approximately 1.78 meters.

To calculate the intensity level at a point 100m from the source, we can use the formula for sound intensity:

I = P / (4 * π * r^2)

where I is the sound intensity, P is the power emitted by the source, and r is the distance from the source.

Given that the power emitted by the source is 40W and the distance is 100m:

P = 40W
r = 100m

We can substitute these values into the formula to find the intensity:

I = 40 / (4 * π * 100^2)
I = 40 / (4 * π * 10,000)
I = 40 / (40,000 * π)
I ≈ 0.000318 W/m^2 (approximately)

Therefore, the intensity level at a point 100m from the source (with no absorption) is approximately 0.000318 W/m^2.

Answer 3

[AI-generated answer — Explain Bot]

To solve this problem, we need to utilize the formula for sound intensity level.

The formula for sound intensity level (L) is:
L = 10 * log10(I/I₀)

Where:
L is the sound intensity level in decibels (dB),
I is the sound intensity in watts per square meter (W/m²),
I₀ is the reference intensity, which is the softest sound heard by the average human ear (approximately 10^(-12) W/m²).

The first step is to find the sound intensity level at a certain distance from the source. We are given that the power emitted by the source is 40W. To find the sound intensity (I) at a certain distance, we can use the equation:

I = P / (4πr²)

Where:
P is the power emitted by the source (40W),
r is the distance from the source in meters.

We can rearrange this equation to solve for I:

I = P / (4πr²)
I = 40 / (4πr²)

Now, we need to find the distance from the source for which the sound level is 90dB. We can rearrange the formula for sound intensity level:

L = 10 * log10(I/I₀)
90 = 10 * log10(I/I₀)

To solve for I, we can rearrange this equation:

log10(I/I₀) = 9

Now, we can rewrite this equation in exponential form:

I/I₀ = 10^9

Finally, we can solve for I:

I = 10^9 * I₀

To calculate the intensity level at a point 100m from the source (assuming no absorption), we can substitute the value of r into the equation I = 40 / (4πr²) and calculate I. Then, we can use the formula for sound intensity level L = 10 * log10(I/I₀) to find the intensity level.

Remember to use the correct value for the reference intensity (I₀) and use the appropriate units for the calculations.