What's the Width of Your Eardrum?

[orgo]

The size of your eardrum partially determines the upper frequency limit of your audible region, usually between 16,000 Hz and 20,000 Hz. If the wavelength is on the order of twice the diameter of the eardrum and the air temperature is 20 degrees Celcius, how wide is your eardrum?

I have no idea how to do this problem. I have looked at the equations for sound, but I don't whether there is an equation that can calculate width.

 

[baffledMatt]

Well, a look in my handy little book of physics formulas tells me that the speed of sound in an ideal gas is:

$$v = \left( \frac{\gamma R T}{\mu}\right)^{1/2}$$

where R is the molar gas constant, T is the temperature, $$\gamma$$ is the ratio of heat capacities and $$\mu$$ is the mean molecular mass. These are all quantities you should be able to find the values of by looking them up.

Now, wavelength is simply wave speed / frequency so you can now calculate the wavelength of the sound and hence estimate the width of the eardrum.

Hope that helps.

Matt

 

[M98Ranger]

Can someone please help me?

Unfortunately, I am not able to provide a specific answer to this question as the width of an individual's eardrum can vary greatly and is not a fixed measurement. Additionally, the upper frequency limit of an individual's audible range is not solely determined by the size of their eardrum, but also by other factors such as the sensitivity of the inner ear and the processing capabilities of the brain. It is best to consult a medical professional for more accurate information about the size of your eardrum and its impact on your hearing capabilities.