Sound Waves: Energy per second

In summary, to calculate how much energy hits each of your eardrums when standing 20m away from a tower generating 2500W of power, we use the equation I=P/(4πr^2) and assume that the speaker generates sound uniformly in a forward hemisphere. Plugging in the values, we get 0.497W/m^2, which when multiplied by the surface area of the eardrum (55mm^2 or 55*10^-6m^2), gives us 2.7*10^-5W. However, note that the sound spreads over a hemisphere, not a sphere, which results in the actual answer of 5.5*10^-5W.
  • #1
Potatochip911
318
3

Homework Statement


Standing 20m away from a tower generating 2500W of power how much energy/s hits each of your eardrums?
Surface area of eardrum=55mm^2
Assume that the speaker generates sound uniformly in a forward hemisphere.

Homework Equations


I=P/(4πr^2)
r=20m
P=2500W


The Attempt at a Solution


I=2500/(4π*20^2)=0.497W/m^2
Surface area of eardrum=55mm^2=55*10^-6m^2
0.497W/m^2*(55*10^-6)m^2=2.7*10^-5W
The actual answer is 5.5*10^-5W, not sure what went wrong.
 
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  • #2
Note that the sound spreads over a hemisphere (not a sphere).
 
  • #3
TSny said:
Note that the sound spreads over a hemisphere (not a sphere).
Oh that's sneaky, I'll have to pay more attention to that stuff in the future.
 

What are sound waves?

Sound waves are a type of mechanical wave that is created by vibrations or disturbances in a medium, such as air or water. These vibrations travel through the medium, carrying energy and creating changes in air pressure, which we perceive as sound.

How is the energy of sound waves measured?

The energy of sound waves is measured in watts, which is a unit of power. Specifically, it is measured as energy per second, or joules per second, as sound waves carry energy through the medium they travel in.

What factors affect the energy of sound waves?

The energy of sound waves can be affected by several factors, including the amplitude of the wave (which determines its loudness), the frequency of the wave (which determines its pitch), and the density and temperature of the medium through which the wave is traveling.

How does the energy of sound waves impact our perception of sound?

The energy of sound waves directly impacts our perception of sound. For example, higher energy waves with larger amplitudes will sound louder to us, while higher frequency waves with more energy will sound higher pitched. The energy of sound waves also determines how far they can travel before dissipating and becoming too faint for us to hear.

What are some practical applications of understanding sound wave energy?

Understanding sound wave energy is important in many fields, including acoustics, music, and engineering. It allows us to design and create better sound systems, improve the quality of audio recordings, and develop technologies like noise-cancelling headphones. In medicine, sound wave energy is also used in ultrasound imaging to visualize internal structures of the body.

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