Calculating Sound Power from Intensity and Distance

In summary, the problem asks for the power radiated by a spherical source that has a sound intensity level of 100 dB at a distance of 9 m. Using the equations for decibels and intensity, the power is calculated to be 10.178 watts.
  • #1
shards5
38
0

Homework Statement



A spherical source radiates sound uniformly in all directions. At a distance of 9 m, the sound intensity level is 100 dB. What power is radiated by this source?

Just a simple answer check to see if my answer is reasonable.

Homework Equations



[tex]\beta[/tex] = 10 db log (I/I0)
Intensity = power/area

The Attempt at a Solution


First convert the given decibels to Intensity then convert the found intensity to power via the second equation.
100 dB = 10 dB log (I/(1*10^-12)
Divide by 10 on both sides.
10 = log ((I/(1*10^-12)
Raise both sides to the tenth power to get rid of log
1010 = (I/(1*10^-12))
Multiple both sides by 1*10-12 I get. . .
I = 0.01 (Can someone confirm that I doesn't have units?)
Plugging in I to the second equation I get. . .
0.01 = [tex]\frac{Power}{4*\pi*9^2}[/tex]
Divide both sides by area I get Power. . .
Power = 10.178 (I know the units should be watt but if Intensity has no units and area only gives m2 then how do I get the units for watt? Does this mean this is wrong?)

Thanks in advance for your help.
 
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  • #2
Hello shards5,
shards5 said:
First convert the given decibels to Intensity then convert the found intensity to power via the second equation.
100 dB = 10 dB log (I/(1*10^-12)
Divide by 10 on both sides.
10 = log ((I/(1*10^-12)
Raise both sides to the tenth power to get rid of log
1010 = (I/(1*10^-12))
Multiple both sides by 1*10-12 I get. . .
I = 0.01 (Can someone confirm that I doesn't have units?)
It does have units! :-p Here, your 1010 figure does not have units because it is a ratio of intensities in terms of power fluxes (a ratio of things with the same units has no units because the units cancel). But I0 Has units! That means your I = 0.01 has units too (which you should be able to figure out going forward from here).

The standard reference sound intensity is

I0 = 1 x 10-12 W/m2

(i.e. units of Watts per square meter).
 
Last edited:
  • #3
Ah, then the whole problem makes sense since m2 cancels out nicely at the end leaving me with just Watts. Thanks a lot!
 

Related to Calculating Sound Power from Intensity and Distance

What is uniform sound?

Uniform sound refers to sound waves that are evenly distributed in terms of frequency and amplitude. This means that there are no sudden changes or fluctuations in the sound, creating a consistent and smooth auditory experience.

How does uniform sound affect our perception?

Uniform sound has been shown to have a calming effect on our perception. When we are exposed to uniform sound, our brain waves synchronize, resulting in a more relaxed and focused state of mind. It can also improve our ability to concentrate and process information.

What are some examples of uniform sound?

Some examples of uniform sound include white noise, pink noise, and brown noise. These types of sounds have a consistent frequency and amplitude, creating a steady background noise. Other examples include the sound of rain, ocean waves, and wind.

Can uniform sound be used for therapeutic purposes?

Yes, uniform sound has been used for therapeutic purposes in a practice known as sound therapy. This involves using specific types of uniform sound to help alleviate symptoms of stress, anxiety, and insomnia. It can also be used to improve focus and concentration.

What is the power of uniform sound?

The power of uniform sound lies in its ability to create a sense of calm and relaxation. It can also help to mask or block out other distracting noises, allowing us to focus on the present moment. Additionally, uniform sound can have a positive impact on our overall mental and emotional well-being.

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