FÁCIL e RÁPIDO 😱 LOGARÍTMO | A escala decibel de som

Summary

In this video, the concept of sound intensity is explored using the decibel scale. The presenter explains how to calculate sound intensity using the formula involving logarithms, providing two examples—one for a sound of 90 decibels and another for a sound of 60 decibels. By substituting values into the formula, the presenter demonstrates how to calculate the corresponding sound intensities and compares the two. The video concludes with an invitation to learn more about logarithms and encourages viewers to stay engaged with the channel for more quality content.

Takeaways

• 😀 The decibel scale is defined by the equation: b = 10 × log(e / e0), where b represents the sound level in decibels, e is the intensity of the sound, and e0 is the reference intensity.
• 😀 The intensity of sound in decibels is a logarithmic measure relative to a reference sound intensity considered to be the faintest detectable by the human ear.
• 😀 The script explains how to calculate the intensity of a sound given its decibel level, starting with 90 decibels.
• 😀 For 90 decibels, the equation is 90 = 10 × log(e1 / e0), and solving for e1 gives e1 = 10^9.
• 😀 In the second example, the sound level is 60 decibels, and the equation is 60 = 10 × log(e2 / e0), leading to e2 = 10^6.
• 😀 A crucial point is that when solving logarithmic equations, base 10 is implicitly assumed if not specified.
• 😀 The script highlights that logarithmic properties allow for simplification, such as canceling terms and working with exponents.
• 😀 When comparing the two intensities, the ratio of e1 to e2 is calculated by dividing 10^9 by 10^6, resulting in 10^3, or 1000.
• 😀 This means the intensity of the first sound is 1000 times greater than the second sound's intensity.
• 😀 The script encourages viewers to continue learning about logarithms and decibels by following the channel for more lessons and quality content.

Q & A

What is the formula for calculating the sound level in decibels?

The formula for calculating the sound level in decibels is: b = 10 log(e / e_0), where 'b' is the sound level in decibels, 'e' is the physical intensity of the sound, and 'e_0' is the reference intensity.

What does the 'e_0' represent in the formula?

'e_0' represents the reference intensity, which is the weakest sound that can be heard by the human ear.

What does the decibel scale measure?

The decibel scale measures the intensity of sound. It compares the intensity of a sound to a reference intensity using a logarithmic scale.

How can we calculate the intensity of sound for 90 decibels?

For 90 decibels, substituting into the formula gives 90 = 10 log(e_1 / e_0). Solving for e_1, we get e_1 = 10^9 e_0, which means the intensity is 10^9 times the reference intensity.

How is the intensity for 60 decibels calculated?

For 60 decibels, substituting into the formula gives 60 = 10 log(e_2 / e_0). Solving for e_2, we get e_2 = 10^6 e_0, meaning the intensity is 10^6 times the reference intensity.

What is the difference in intensity between 90 dB and 60 dB?

The intensity at 90 dB is 1000 times greater than at 60 dB. This is calculated by comparing the ratios e_1 / e_2 = 10^9 / 10^6 = 10^3 = 1000.

Why do we use logarithms to calculate sound intensity in decibels?

Logarithms are used in decibel calculations because the human ear perceives sound intensity on a logarithmic scale, meaning sound intensity increases exponentially, not linearly.

What does the expression 'log' in the formula represent?

The 'log' in the formula represents the logarithm to the base 10, which is used to scale the difference in sound intensities in a manageable way.

Can the formula for sound level in decibels be simplified?

Yes, when calculating, the 10 in front of the logarithm and the base 10 of the logarithm can simplify calculations, particularly when using exponential notation for the intensities.

What is the importance of the reference intensity e_0 in this calculation?

The reference intensity e_0 is crucial because it sets a baseline for comparison. The intensity of any given sound is measured relative to this baseline, which represents the faintest sound that can be heard by the average human ear.