Sound waves and eardrum problem

[thschica]

A 50 dB sound wave strikes an eardrum whose area is 4.1 * 10-5 m2.
(a) How much energy is absorbed by the eardrum per second?
W
(b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?
years

I have tried to solve using I=2pi^2f^2A^2pv

and got f=280 ; v=343;p=1.29;I=1*10^-12 and A =1.28e-18 its wrong though

 

[Andrew Mason]

A 50 dB sound wave strikes an eardrum whose area is 4.1 * 10-5 m2.
(a) How much energy is absorbed by the eardrum per second?
W
(b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?
years

I have tried to solve using I=2pi^2f^2A^2pv

and got f=280 ; v=343;p=1.29;I=1*10^-12 and A =1.28e-18 its wrong though

Decibels are a little tricky to work with. I think all you need to know is that $I = 10 log(P/P_0)$ where P is the power/area and $P_0 = 10^{-12} W/m^2$

AM

 

[kyle8921]

I can provide a more accurate and detailed response to the given content.

Firstly, it is important to note that sound waves are a form of mechanical energy that travels through a medium, such as air or water. When these waves reach our eardrums, they cause it to vibrate, which is then transmitted to the inner ear and eventually to the brain, allowing us to perceive sound.

Now, let's address the given scenario. A 50 dB sound wave means that the intensity of the sound wave is 50 decibels, which is equivalent to 0.00001 watts per square meter (W/m^2). The eardrum has an area of 4.1 * 10^-5 m^2, so we can calculate the energy absorbed by the eardrum per second using the formula:

Energy = intensity x area

Therefore, the energy absorbed by the eardrum per second is:

Energy = (0.00001 W/m^2) x (4.1 * 10^-5 m^2) = 4.1 * 10^-10 W

To calculate how long it would take for the eardrum to receive a total energy of 1.0 J, we can use the formula:

Time = energy/absorbed energy per second

Therefore, the time taken for the eardrum to receive a total energy of 1.0 J is:

Time = (1.0 J)/(4.1 * 10^-10 W) = 2.4 * 10^9 seconds

This is equivalent to approximately 76 years. This calculation assumes that the eardrum can continuously absorb the energy without any damage, which is not the case in reality. Our ears have protective mechanisms, such as the reflexive contraction of the middle ear muscles, to prevent excessive sound energy from damaging our eardrums.

In conclusion, sound waves and eardrums are complex and fascinating subjects in the field of acoustics. As a scientist, it is important to understand the properties of sound waves and how they interact with our eardrums in order to protect our hearing and study the world of sound.