Intensity of sound wave and energy

The area of a circle is πr^2, not π(d/2)^2. Also, make sure your units are consistent. The unit of intensity is W/m^2, so the unit of energy should be J/m^2. In summary, to calculate the energy transferred to your eardrum while listening to a sound with intensity 2x10^(-3) W/m^2 for 1.0 min, you would first need to calculate the area of your eardrum, which is 2.83x10^-5 m^2. Then, using the equation P=IA, you would get a power of 5.66x10^-8 W. Finally, using the equation P=delta
  • #1
Pambos
1
0

Homework Statement



A sound wave with intensity 2x10^(-3) W/m^2 is perceived to be modestly loud. Your eardrum is 6.0 mm in diameter. How much energy will be transferred to your eardrum while listening to this sound for 1.0 min?

Homework Equations


P=IA=(intensity)(area)
=2x10^(-3) * (pi (6x10^-3)^2)
=2.2610x10^-7 W

The Attempt at a Solution


P=IA=(intensity)(area)
=2x10^(-3) * (pi (6x10^-3)^2)
=2.2610x10^-7 W

P=delta E/ delta t
=2.2610x10^-7 J/s * 60 s
=1.3572x10^-5 J

..its not the correct answer can anyone help?
 
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  • #2
Hi Pambos, Welcome to Physics Forums!

Check your area calculation.
 

FAQ: Intensity of sound wave and energy

What is the relationship between intensity of sound wave and energy?

The intensity of a sound wave is directly proportional to the energy it carries. This means that as the intensity increases, so does the energy of the sound wave. This relationship is represented by the equation: I ∝ E, where I is the intensity and E is the energy.

How is the intensity of a sound wave measured?

The intensity of a sound wave is typically measured in decibels (dB). This scale is logarithmic, meaning that a small change in decibels represents a large change in intensity. The standard reference point for measuring sound intensity is 0 dB, which is the threshold of human hearing.

What factors affect the intensity of a sound wave?

The intensity of a sound wave can be affected by several factors, including the amplitude of the wave (how high or low it is), the distance from the source of the sound, and the medium through which the sound travels. For example, the intensity of a sound will decrease as the distance from the source increases, and it will also be affected by the density and temperature of the medium it travels through.

How does the intensity of a sound wave relate to its perceived loudness?

The perceived loudness of a sound is not directly proportional to its intensity. In fact, the human ear perceives sound intensity on a logarithmic scale, meaning that we perceive a doubling of intensity as a small increase in loudness. This is why a sound that is twice as loud as another sound may only be perceived as slightly louder.

Can the intensity of a sound wave be harmful?

Yes, high intensity sound waves can be harmful to human hearing. Prolonged exposure to sounds above 85 dB can lead to hearing loss. In addition, very high intensity sound waves, such as those from explosions or jet engines, can cause physical damage to the ear and other parts of the body.

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