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: Sound Level Calculation
**Problem Statement:**
What is the sound level (in decibels) of a sound whose intensity is \(7.5 \times 10^{-8} \, \text{W/m}^2\)?
**Options:**
- ⦾ 6.7 dB
- ⦾ 7.5 dB
- ⦾ 80 dB
- ⦾ 67 dB
### Explanation:
To calculate the sound level in decibels (dB), use the formula:
\[ L = 10 \log_{10} \left( \frac{I}{I_0} \right) \]
where:
- \( L \) is the sound level in decibels (dB),
- \( I \) is the intensity of the sound in watts per square meter (\(\text{W/m}^2\)),
- \( I_0 \) is the reference intensity, typically \( 1 \times 10^{-12} \, \text{W/m}^2 \).
Given the intensity (\( I \)) is \( 7.5 \times 10^{-8} \, \text{W/m}^2 \), substitute the values into the formula:
\[ L = 10 \log_{10} \left( \frac{7.5 \times 10^{-8}}{1 \times 10^{-12}} \right) \]
Simplify the fraction inside the logarithm:
\[ \frac{7.5 \times 10^{-8}}{1 \times 10^{-12}} = 7.5 \times 10^4 \]
Now calculate the logarithm:
\[ \log_{10} (7.5 \times 10^4) = \log_{10} (7.5) + \log_{10} (10^4) \]
\[ = \log_{10} (7.5) + 4 \]
The approximate value of \( \log_{10} (7.5) \) is around 0.875.
Therefore, the sound level calculation becomes:
\[ L = 10 \times (0.875 + 4) \]
\[ = 10 \times 4.875 \]
\[ = 48.75 \, \text{dB} \]
Since this value is not in the given options,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3fc0f41c-1d8b-41a4-aee9-3a82e03a5afd%2F13ba3319-9566-4771-8c91-cc8653e73d36%2F1lzo8jr.png&w=3840&q=75)
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