Calculation for finding distance with regard to sound intensity

Click For Summary
SUMMARY

The discussion focuses on calculating the distance from a sound source where the sound intensity from Amplifier 2 (maximum power output of 175 W) equals the sound level of Amplifier 1 (fixed power output of 300 W, producing 121.15 dB). Key equations used include A=4 x Pi x r^2 for surface area, I=P/A for intensity, and dB=10log(I/Io) for sound level. Participants clarify the relationship between power density, area, and distance, concluding that as the radius increases, the intensity decreases proportionally to the area, leading to a definitive understanding of how to calculate the required distance.

PREREQUISITES
  • Understanding of sound intensity and decibel levels
  • Familiarity with the equations for area and intensity (A=4 x Pi x r^2, I=P/A)
  • Basic knowledge of logarithmic functions and their application in sound level calculations
  • Concept of energy density in relation to distance from a sound source
NEXT STEPS
  • Study the relationship between sound intensity and distance using the inverse square law
  • Explore the effects of different power outputs on sound levels in practical scenarios
  • Learn about sound wave propagation and its impact on audio engineering
  • Investigate the application of logarithmic scales in various fields beyond acoustics
USEFUL FOR

Acoustics students, audio engineers, sound technicians, and anyone interested in understanding sound intensity and its relationship to distance from a sound source.

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