A law of physics states that the intensity of sound is inversely proportional to the square of the distance d from the source: I- k/d?. (a) If B, is the decibel level at a distance d, use this model and the equation B- 10 log to (described in this section) to find the equation for the decibel level B2 at a distance dz relative to B, and d B2- (b) The Intensity level at a rock concert is 125 dB at a distance 2.7 m from the speakers. Find the intensity level at a distance of 10 m. (Round your answer to the nearest whole number.) B2 = dB
A law of physics states that the intensity of sound is inversely proportional to the square of the distance d from the source: I- k/d?. (a) If B, is the decibel level at a distance d, use this model and the equation B- 10 log to (described in this section) to find the equation for the decibel level B2 at a distance dz relative to B, and d B2- (b) The Intensity level at a rock concert is 125 dB at a distance 2.7 m from the speakers. Find the intensity level at a distance of 10 m. (Round your answer to the nearest whole number.) B2 = dB
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Concept explainers
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
![### Understanding Sound Intensity and Distance
A law of physics states that the intensity of sound is inversely proportional to the square of the distance from the source: \( I = \frac{k}{d^2} \).
- \( I \) represents the intensity of the sound.
- \( k \) is a constant specific to the sound source.
- \( d \) is the distance from the sound source.
#### Problem Statement
(a) **Finding the Decibel Equation**
If \( B_1 \) is the decibel level at a distance \( d_1 \), use the following model and equation to find the decibel level \( B_2 \) at a distance \( d_2 \) relative to \( B_1 \) and \( d_1 \):
\[
B = 10 \log \frac{I}{I_0}
\]
Where:
- \( B \) is the decibel level.
- \( I \) is the intensity of the sound.
- \( I_0 \) is a reference intensity.
#### Solution:
To find the equation for \( B_2 \):
\[
B_2 =
\]
(b) **Application: Rock Concert Intensity**
The intensity level at a rock concert is 125 dB at a distance of 2.7 m from the speakers. Find the intensity level at a distance of 10 m. (Round your answer to the nearest whole number.)
\[
B_2 = \_\_\_\_\_ \text{ dB}
\]
### Key Concepts Explained
Decibels provide a logarithmic measure of sound intensity. The formula \( B = 10 \log \frac{I}{I_0} \) allows us to compare sound intensities at different distances. By understanding this relationship, we can calculate how sound intensity diminishes with increasing distance from the source.
### Example Calculation
Given:
- Initial intensity level \( B_1 = 125 \) dB at \( d_1 = 2.7 \) m,
- Find \( B_2 \) at \( d_2 = 10 \) m.
Using the properties of logarithms and the inverse square law of sound intensity will help us derive the new intensity level.
### Graphs and Diagrams
No specific graphs or diagrams are provided in the image. Detailed steps and calculations would typically accompany this explanation in a classroom or textbook setting, potentially including a graph](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5451aef3-1a55-4404-bb01-8f8933157334%2Fbbeb9007-62a9-4d37-b731-fb1d19278d0f%2Fut3fe4c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Sound Intensity and Distance
A law of physics states that the intensity of sound is inversely proportional to the square of the distance from the source: \( I = \frac{k}{d^2} \).
- \( I \) represents the intensity of the sound.
- \( k \) is a constant specific to the sound source.
- \( d \) is the distance from the sound source.
#### Problem Statement
(a) **Finding the Decibel Equation**
If \( B_1 \) is the decibel level at a distance \( d_1 \), use the following model and equation to find the decibel level \( B_2 \) at a distance \( d_2 \) relative to \( B_1 \) and \( d_1 \):
\[
B = 10 \log \frac{I}{I_0}
\]
Where:
- \( B \) is the decibel level.
- \( I \) is the intensity of the sound.
- \( I_0 \) is a reference intensity.
#### Solution:
To find the equation for \( B_2 \):
\[
B_2 =
\]
(b) **Application: Rock Concert Intensity**
The intensity level at a rock concert is 125 dB at a distance of 2.7 m from the speakers. Find the intensity level at a distance of 10 m. (Round your answer to the nearest whole number.)
\[
B_2 = \_\_\_\_\_ \text{ dB}
\]
### Key Concepts Explained
Decibels provide a logarithmic measure of sound intensity. The formula \( B = 10 \log \frac{I}{I_0} \) allows us to compare sound intensities at different distances. By understanding this relationship, we can calculate how sound intensity diminishes with increasing distance from the source.
### Example Calculation
Given:
- Initial intensity level \( B_1 = 125 \) dB at \( d_1 = 2.7 \) m,
- Find \( B_2 \) at \( d_2 = 10 \) m.
Using the properties of logarithms and the inverse square law of sound intensity will help us derive the new intensity level.
### Graphs and Diagrams
No specific graphs or diagrams are provided in the image. Detailed steps and calculations would typically accompany this explanation in a classroom or textbook setting, potentially including a graph
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