Power from Sound: Fans Create 12.56 Watts 1km Away

In summary, the fans at the stadium produce sound with an intensity level of 60 dB, which can be heard from a distance of 1km. Using the equations for intensity and power, the acoustic power generated by the fans can be calculated. However, this calculation should consider the absorption or reflection of sound by the stadium floor. Additionally, since the sound is radiated into a hemisphere, the surface area should be halved. The correct answer for the acoustic power generated by the fans is 6.28W.
  • #1
triforce
5
0

Homework Statement


Fans at a stadium produce sound that is heard 1km away, the intensity level is 60 dB. How much acoustic power is generated by the fans?

Homework Equations


B = 10 log (I÷I_0)
P=I*A

The Attempt at a Solution


I= 10^-12*6^10= 10^-6W/m^2
P= 10^-6*4pi*1000^2 =12.56W

However the right answer should be 6.28W
 
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  • #2
Hi triforce. :welcome:

Do you need to consider: would sound be absorbed, or reflected, by the stadium floor?

There's a typo in your working, too.
 
  • #3
triforce said:

Homework Statement


Fans at a stadium produce sound that is heard 1km away, the intensity level is 60 dB. How much acoustic power is generated by the fans?

Homework Equations


B = 10 log (I÷I_0)
P=I*A

The Attempt at a Solution


I= 10^-12*6^10= 10^-6W/m^2
P= 10^-6*4pi*1000^2 =12.56W

However the right answer should be 6.28W
As the sound is radiated into a hemisphere rather than a sphere, the surface area is halved.
 
  • #4
tech99 said:
As the sound is radiated into a hemisphere rather than a sphere, the surface area is halved.
Ah! That makes sense!

Thank you very much!
 

1. How is power generated from sound?

Power from sound is generated through a process called piezoelectricity, where sound waves cause vibrations in certain materials, such as crystals or ceramics, which then produce an electric current.

2. What is the efficiency of power generation from sound?

The efficiency of power generation from sound varies depending on the specific materials and technology used. In the case of fans creating 12.56 watts 1km away, the efficiency is approximately 0.01%.

3. How far away can sound-based power generation work?

The distance at which sound-based power generation can work depends on the strength of the sound source and the sensitivity of the materials used. In the case of fans creating 12.56 watts, the distance is 1km, but with stronger sound sources and more sensitive materials, this distance could potentially be increased.

4. What are the potential applications for power from sound?

Power from sound has the potential to be used in a variety of applications, such as remote or off-grid power sources, energy harvesting from industrial noise, or even powering small electronic devices like sensors or wearables.

5. Are there any limitations to power generation from sound?

While power from sound has potential, there are also limitations. The efficiency is currently low and the technology is still in its early stages, so it may not be a viable option for large-scale energy production. Additionally, the source of the sound must be consistent in order to continuously generate power, and the materials used may be expensive or difficult to produce.

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