Compute the sound intensity level in decibels for each sound listed in Table 3.21.

Name: Problem 51, Chapter 3: Precalculus: Graphical, Numerical, Algebraic
Uploaded: 2020-02-29T17:14:53-08:00
Duration: 4 min 22 s
Channel: Heather Zimmers
Description: Compute the sound intensity level in decibels for each sound listed in Table 3.21.

Compute the sound intensity level in decibels for each sound...

Key Concepts

Sound Intensity

This concept refers to the amount of sound power passing through a unit area, usually expressed in watts per square meter. It is fundamental in acoustics as it quantifies how much energy a sound wave carries, which affects how loud the sound is perceived.

Decibel (dB) Scale

The decibel is a logarithmic unit used to express the ratio of a particular sound intensity to a reference intensity. It simplifies the handling of very large or very small numbers and reflects the logarithmic way in which the human ear perceives sound differences.

Logarithmic Calculation

The use of logarithms, typically with a base of 10, is essential in converting the ratio of sound intensities into decibels. This mathematical operation compresses the vast range of audible sound intensities into a more manageable scale for analysis and comparison.

Reference Intensity

Reference intensity is the baseline or standard value against which sound intensity is compared when calculating decibel levels. It is commonly set at 1x10^-12 watts per square meter, which approximates the threshold of human hearing.

Transcript

00:01 In this problem, we're calculating the sound intensity in decibels for a variety of sounds, and we're using this formula here, which relates to the level of sound density with the intensity of the sound and the intensity of the quietest audible sound.

00:20 And we have to go back into section 3 .3 to find that formula.

00:25 Okay, so for part a, we have a hearing threshold, which has a sound intensity level of i equals 10 to the next number.

00:32 Negative 12th.

00:34 So to find the level of sound in decibels, which we're calling beta, we're going to substitute the value of i into the equation, and we're going to substitute 10 to the negative 12th in for i -0.

00:50 And now we can simplify because 10 to the negative 12th over 10 to the negative 12th is just one.

00:57 And keep simplifying.

00:59 The log of 1 is 0, so we have 10 times 0, so it's just 0.

01:04 So it's just zero decibels.

01:06 Zero decibels is the hearing threshold.

01:12 That's kind of like our starting place.

01:16 From there we get gradually louder sounds.

01:19 The next one is rustling leaves and the intensity is 10 to the negative 11th so we can substitute that in to our formula and we're still going to substitute in every time 10 to the negative 12th for the barely audible sound as i not.

01:36 Simplify and what we want to do here is subtract the power on 10, and that gives us 10 to the first.

01:45 10 to the first is just 10.

01:47 And the log of 10 is 1, so we have 10 times 1, which is 10.

01:52 So the sound intensity is 10 decibels for rustling leaves.

02:03 The next one is conversation, where the sound intensity is 10 to the negative 6th.

02:13 So we substitute that in over 10 to the negative 1th...

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