Power output and sound intensity

  • #1
dylanwalt
6
4
Homework Statement
At a distance of 2.5m from your stereo system with two speakers, the intensity level is 78 dB. Assume that all the energy from the amplifier goes into producing sound. What power output does your stereo have?
Relevant Equations
B=10log I/Ith
In the picture below
sideways speakers 01.jpg
 

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  • #2
Why did you change ##4\pi r^2## to ##\pi r^2##?
 
  • #3
We're assuming the two speakers are point sources that share the same location?
 
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  • #4
Mister T said:
We're assuming the two speakers are point sources that share the same location?
Good point. More likely, the speakers are 2.5m either side of the listener.
 
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  • #5
haruspex said:
Why did you change ##4\pi r^2## to ##\pi r^2##?
I was not sure if the question was in 2d hence pi*r*r or 3d 4*pi*r*r.
 
  • #6
haruspex said:
Good point. More likely, the speakers are 2.5m either side of the listener.
I’m not 100% sure it is a vague question. I assumed they were in the same speaker housing maybe one was bass and one treble etcetera.
 
  • #7
dylanwalt said:
I was not sure if the question was in 2d hence pi*r*r or 3d 4*pi*r*r.
We do not live in Flatland.
dylanwalt said:
I’m not 100% sure it is a vague question. I assumed they were in the same speaker housing maybe one was bass and one treble etcetera.
It mentions specifically "two speakers", and stereo systems are not just a matter of separate woofers and tweeters; typically, a stereo system has two speaker housings, each containing a tweeter and a woofer.
The separation of stereo speakers would commonly be around 2.5m, suggesting an equilateral triangle arrangement.
However, it's not clear to me how that would affect the answer, so just take it as a point source.
 
  • #8
haruspex said:
The separation of stereo speakers would commonly be around 2.5m, suggesting an equilateral triangle arrangement.
However, it's not clear to me how that would affect the answer, so just take it as a point source.
Yeah, this is a very confusing problem statement.

haruspex said:
We do not live in Flatland.
LOL. :smile:
 
  • #9
dylanwalt said:
I was not sure if the question was in 2d hence pi*r*r or 3d 4*pi*r*r.
Please check your Private Messages (PMs) in a minute or two. I will send you some tips for learning and using LaTeX to post math equations at PF. :wink:
 
  • #10
Speaker cabinets contain at least one driver, like say a woofer and a tweeter. By their very design they are not point sources. In my opinion that's the most unrealistic feature of the problem statement.
 

Related to Power output and sound intensity

What is the relationship between power output and sound intensity?

Power output refers to the amount of energy a sound source emits per unit of time, measured in watts (W), while sound intensity is the amount of sound power passing through a unit area, measured in watts per square meter (W/m²). The relationship is direct; as the power output of a sound source increases, the sound intensity also increases, assuming the distance from the source remains constant.

How is sound intensity level measured and what units are used?

Sound intensity level is measured using a logarithmic scale called decibels (dB). It is calculated using the formula: L = 10 log(I/I₀), where L is the sound intensity level in decibels, I is the sound intensity, and I₀ is the reference sound intensity, typically 1 picowatt per square meter (1 pW/m²).

What factors affect sound intensity?

Several factors affect sound intensity, including the power output of the sound source, the distance from the sound source, and the medium through which the sound travels. Sound intensity decreases with increasing distance from the source due to the spreading of sound waves. Additionally, absorption and scattering by the medium can reduce sound intensity.

How does distance from the sound source affect sound intensity?

Sound intensity decreases with the square of the distance from the sound source. This relationship is described by the inverse square law, which states that if you double the distance from the sound source, the sound intensity is reduced to one-quarter of its original value. Mathematically, I ∝ 1/r², where I is the sound intensity and r is the distance from the source.

Can sound intensity be harmful to human hearing, and if so, at what levels?

Yes, sound intensity can be harmful to human hearing. Prolonged exposure to sound intensity levels above 85 decibels (dB) can cause hearing damage. Sound levels above 120 dB can cause immediate harm, including pain and potential hearing loss. It is important to use hearing protection in environments where sound intensity levels exceed these thresholds.

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