Calculation for finding distance with regard to sound intensity

Click For Summary

Homework Help Overview

The discussion revolves around calculating the distance from a sound source necessary to achieve a specific sound level, comparing two amplifiers with different power outputs. The subject area includes sound intensity, decibel levels, and the relationship between power, area, and distance in sound propagation.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between sound intensity and distance, questioning how to relate power output to distance using relevant equations. There is discussion about the implications of doubling the radius on power density and area.

Discussion Status

Participants are actively engaging with the concepts, clarifying misunderstandings about energy density and area. Some have begun to connect their reasoning to the original problem, indicating progress in understanding the relationships involved.

Contextual Notes

There is an emphasis on understanding the equations related to sound intensity and the geometry of sound propagation, with participants grappling with the implications of these equations in the context of the problem.

Aleisha
Messages
25
Reaction score
0

Homework Statement


Two amplifiers can be used to power a sound system.
Amplifier 1: Has a fixed power output of 300 W.
Amplifier 2: Has a variable power output of between 15 W and 175 W.
You may assume that the power output of the amplifier is equal to the power of the sound waves that are produced.
The speaker is disconnected from Amplifier 1 and is instead connected to Amplifier 2, which is operated at maximum power.
Previous calculated question sound level of amplifier 1= 121.15 dB
Calculate how close to the speaker must you stand for the sound level to be the same as when the speaker was connected to Amplifier 1.

Homework Equations


A=4 x Pi x r^2
I=P/A
dB=10log(I/Io)

The Attempt at a Solution


I want to calculate a distance, so the the sound decibel of amplifier 2 (121.15 dB) will equal amplifier 1.
I don't know an equation with distance that would relate to the equations above.
 
Physics news on Phys.org
Aleisha said:
I don't know an equation with distance that would relate to the equations above
Yet you managed to quote an equation which is relevant.
When sound has traveled a distance r from its source, how thinly is its power spread?
 
haruspex said:
Yet you managed to quote an equation which is relevant.
When sound has traveled a distance r from its source, how thinly is its power spread?
Right ofcourse I didn’t realize I was looking for radius. Don’t i need to know the area to get the radius? Or could I equate the two equations together?
 
Aleisha said:
Right ofcourse I didn’t realize I was looking for radius. Don’t i need to know the area to get the radius? Or could I equate the two equations together?
A wavefront from the source forms an expanding sphere. The power is spread out over the surface of the sphere. As the radius doubles, what happens to the power density?
 
The power density will increase by a factor of 4, if the radius is doubled?
 
Aleisha said:
The power density will increase by a factor of 4, if the radius is doubled?
Power density is power per unit area. The power total is constant. If the radius doubles what happens to the area?
 
Ohhh the area is 1/4 of the original amplifier?
 
Aleisha said:
Ohhh the area is 1/4 of the original amplifier?
No.
Consider a single pulse of sound emitted from a point source. After some time it has traveled a distance r, so the wavefront forms a spherical shell radius r centred on the source. The total energy in the pulse is spread evenly over the shell, producing a certain energy density, ρ. The same time again later it has expanded to radius 2r. What is the energy density now?
 
Twice as large
 
  • #10
Aleisha said:
Twice as large
The total energy is the same. It is spread over a larger area.
Do you understand the concept of density?
 
  • Like
Likes   Reactions: Aleisha
  • #11
It must be half then? That’s what I thought I meant because if 1/4 because the radius its r squared not just r... I’m getting too confused haha
 
  • #12
Aleisha said:
It must be half then?
That is moving in the right direction, but as you say it is radius squared, not half but ...?
(I have the feeling that you have, in your mind, already given the right answer but kept writing it down wrongly.)
 
  • #13
haruspex said:
That is moving in the right direction, but as you say it is radius squared, not half but ...?
(I have the feeling that you have, in your mind, already given the right answer but kept writing it down wrongly.)
Ah ha! It’s 4 times bigger!
 
  • #14
Aleisha said:
Ah ha! It’s 4 times bigger!
What is four times bigger, the area or the energy density?
 
  • #15
haruspex said:
What is four times bigger, the area or the energy density?
It must be the area according to the equation A=4 x Pi x r^2
 
  • #16
Aleisha said:
It must be the area according to the equation A=4 x Pi x r^2
Right, so what happens to the energy density?
 
  • #17
I=P/A If the area is four times bigger then the intensity (energy density) then the intensity with decrease by 4 times, correct?
 
  • #18
Aleisha said:
I=P/A If the area is four times bigger then the intensity (energy density) then the intensity with decrease by 4 times, correct?
Right.
So can you now answer the question in post #1?
 
  • #19
Yes yes! Thank you I get the correlation now :)
 

Similar threads

Waves: Calculate the sound intensity from two speakers
  • · Replies 3 ·
Replies
3
Views
3K
Audio interference of sound waves from two speakers
  • · Replies 19 ·
Replies
19
Views
4K
Calculating Sound Intensity and Pressure Variation at a Distance
  • · Replies 4 ·
Replies
4
Views
2K
Sound intensity of a thunderbolt
  • · Replies 1 ·
Replies
1
Views
1K
Ratio of Intensities of 2 sounds
  • · Replies 5 ·
Replies
5
Views
2K
Calculating τ by knowing I is proportional to A^2
  • · Replies 8 ·
Replies
8
Views
2K
Max velocity of a vibrating loud speaker membrane given sound intensity
  • · Replies 4 ·
Replies
4
Views
2K
What is the relationship between power in watts and power in dBW?
  • · Replies 11 ·
Replies
11
Views
3K
Calculating the power output from a persons mouth
  • · Replies 3 ·
Replies
3
Views
2K
What is the decibel level of a sound at 4% intensity of a 95dB sound?
  • · Replies 2 ·
Replies
2
Views
2K