A sound power level reading of 127 dB was taken near a construction site
where chippers were being used. When all but one of the chippers stopped working,
the sound power level reading was 120 dB. Estimate the number of chippers in
operation when the reading of 127 was obtained. Assume that the sources
may be treated as ideal point sources located at the same point.
7 dB higher sound level (initially) corresponds to an intensity ratio I1/I2 given by
10*Log(10)I1/I2 = 7
Log(10)I1/I2 = 0.7
I1/I2 = 10^0.7 = 5.0
There were 5 chippers working initially
thanks!
To estimate the number of chippers in operation when the reading of 127 dB was obtained, we can use the inverse square law for sound intensity.
The inverse square law states that the sound intensity decreases with the square of the distance from the source. However, in this case, since we are assuming the sources are located at the same point, we can consider the distance as constant throughout the measurements.
According to the inverse square law, the sound intensity level (SIL) at a certain distance from the source can be calculated using the formula:
SIL2 = SIL1 + 20 * log10(d1/d2)
Where SIL1 is the sound intensity level at the reference distance (SIL1 = 120 dB), SIL2 is the sound intensity level at the desired distance (SIL2 = 127 dB), d1 is the reference distance, and d2 is the desired distance.
Let's assume the reference distance (d1) is 1 chipper and the desired distance (d2) is the unknown number of chippers in operation when the reading of 127 dB was obtained.
Now we can plug in the values and solve for the unknown number of chippers:
127 = 120 + 20 * log10(1/N)
Where N is the unknown number of chippers.
127 - 120 = 20 * log10(1/N)
7 = 20 * log10(1/N)
log10(1/N) = 7/20
1/N = 10^(7/20)
N = 10^(7/20)
Using a calculator, we find that N is approximately 3.98.
Since the number of chippers cannot be fractional, we round the answer to the nearest whole number.
Therefore, the estimated number of chippers in operation when the reading of 127 dB was obtained is 4.
To estimate the number of chippers in operation when the sound power level reading of 127 dB was obtained, we can use the concept of the inverse square law for sound propagation.
The inverse square law states that the intensity of sound decreases in proportion to the square of the distance from the source. In other words, as you move further away from a sound source, the sound intensity decreases.
Here's how we can use the inverse square law to solve this problem:
1. Convert the sound power level readings (dB) into sound intensity levels (dBIL). Since the chippers are assumed to be ideal point sources located at the same point, their sound intensity remains constant regardless of the number of chippers in operation.
- For the first reading of 127 dB, the sound intensity level (dBIL1) is 127 dB.
- For the second reading of 120 dB, the sound intensity level (dBIL2) is 120 dB.
2. Apply the inverse square law formula to relate the sound intensity levels and the distance from the source:
dBIL1 - dBIL2 = 20 * log10(D2/D1)
(where D1 is the distance for the first reading, and D2 is the distance for the second reading)
3. Rearrange the formula to solve for the distance ratio (D2/D1):
D2/D1 = 10^((dBIL1 - dBIL2)/20)
4. Since the sound intensity level remains constant, the distance ratio can be used to estimate the number of chippers in operation. As mentioned earlier, the sound intensity level decreases with distance squared. Thus, the distance ratio squared would approximately relate to the number of chippers:
Number of chippers = (D2/D1)^2
By plugging in the values, we can calculate the approximate number of chippers in operation.