Find the number of decibels of sound produced by a jet engine at a distance of 50 metres if the intensity is 10 watts per square metre.
To find the number of decibels (dB) of sound produced by a jet engine at a distance of 50 metres with an intensity of 10 watts per square metre, we can use the following formula:
dB = 10 * log10(I/I0)
where:
- dB is the number of decibels
- I is the sound intensity in watts per square metre
- I0 is the reference sound intensity (usually taken as 10^(-12) W/m^2)
First, let's calculate the reference sound intensity:
I0 = 10^(-12) W/m^2
Next, we substitute the given values into the formula:
dB = 10 * log10(10/10^(-12))
To simplify the calculation, let's first calculate the logarithm part:
log10(10/10^(-12)) = log10(10) - log10(10^(-12))
Since log10(10) = 1 and log10(10^(-12)) = -12, we have:
log10(10/10^(-12)) = 1 - (-12)
= 1 + 12
= 13
Plugging this value back into the formula:
dB = 10 * 13
= 130
Therefore, the number of decibels of sound produced by the jet engine at a distance of 50 metres with an intensity of 10 watts per square metre is 130 dB.
To find the number of decibels (dB) of sound produced by a jet engine, you can use the formula:
dB = 10 * log10(I/I0)
where I is the sound intensity in watts per square meter and I0 is the reference intensity.
Given that the sound intensity is 10 watts per square meter, and we need to find the number of decibels at a distance of 50 meters, we need to consider the inverse square law for sound propagation.
The inverse square law states that the sound intensity decreases with the square of the distance. So, if the intensity at a reference distance D0 is I0, then at a distance D, the intensity can be calculated using the formula:
I = I0 * (D0^2 / D^2)
In this case, the distance D0 is not provided, so we'll assume it is the distance at which the reference intensity I0 is specified.
Let's calculate the reference intensity I0 first. Let's assume it is specified at a distance of 1 meter.
I0 = 10 watts per square meter
Now, we can calculate the actual intensity I at a distance of 50 meters using the formula mentioned above:
I = I0 * (D0^2 / D^2)
I = 10 * (1^2 / 50^2)
I = 10 / 2500
I = 0.004 watts per square meter
Now, we can calculate the number of decibels:
dB = 10 * log10(I/I0)
dB = 10 * log10(0.004/10)
dB = 10 * log10(0.0004)
dB ≈ 10 * (-3.4)
dB ≈ -34
Therefore, the number of decibels produced by the jet engine at a distance of 50 meters is approximately -34 dB.