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)
Any one pls
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.
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.