A jet engine emits sound uniformly in all directions, radiating an acoustic power of 2.19 x 10 W. Find the intensity I of the sound at a distance of 51.9 m from the engine and calculate the corresponding sound intensity level ß. I = W/m? dB
Properties of sound
A sound wave is a mechanical wave (or mechanical vibration) that transit through media such as gas (air), liquid (water), and solid (wood).
Quality Of Sound
A sound or a sound wave is defined as the energy produced due to the vibrations of particles in a medium. When any medium produces a disturbance or vibrations, it causes a movement in the air particles which produces sound waves. Molecules in the air vibrate about a certain average position and create compressions and rarefactions. This is called pitch which is defined as the frequency of sound. The frequency is defined as the number of oscillations in pressure per second.
Categories of Sound Wave
People perceive sound in different ways, like a medico student takes sound as vibration produced by objects reaching the human eardrum. A physicist perceives sound as vibration produced by an object, which produces disturbances in nearby air molecules that travel further. Both of them describe it as vibration generated by an object, the difference is one talks about how it is received and other deals with how it travels and propagates across various mediums.
![**Question:**
A jet engine emits sound uniformly in all directions, radiating an acoustic power of \(2.19 \times 10^5 \, \text{W}\). Find the intensity \(I\) of the sound at a distance of \(51.9 \, \text{m}\) from the engine and calculate the corresponding sound intensity level \(\beta\).
**Answer:**
\(I = \, \_\_\_\_ \, \text{W/m}^2\)
\(\beta = \, \_\_\_\_ \, \text{dB}\)
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**Explanation for Students:**
This problem asks you to determine the sound intensity and intensity level at a given distance from a jet engine, which is emitting sound equally in all directions.
1. **Identify Given Information:**
- Acoustic power (\(P\)) = \(2.19 \times 10^5 \, \text{W}\)
- Distance (\(r\)) = \(51.9 \, \text{m}\)
2. **Calculate Intensity (\(I\)):**
- Sound intensity is given by the formula:
\[
I = \frac{P}{A}
\]
- Where \(A\) is the surface area over which the sound is spreading. For a sphere, \(A = 4\pi r^2\).
- Substitute the given values into the formula.
3. **Calculate Sound Intensity Level (\(\beta\)):**
- Sound intensity level in decibels (dB) is calculated using:
\[
\beta = 10 \log_{10}\left(\frac{I}{I_0}\right)
\]
- Where \(I_0 = 10^{-12} \, \text{W/m}^2\) is the reference intensity. Substitute the calculated intensity into this formula to find \(\beta\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F568ff014-20eb-4de5-8e14-1d7fe4707f89%2F0f4ca93c-771e-439a-9af1-aa11c069dbb9%2F7wlh6g.jpeg&w=3840&q=75)
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