Audible frequency in xenon gas, .

[connorty541]

You come to a landing on Congress. Actually, it was more a splash-down than a landing as Congress is made up of mostly ocean. Consulting your favorite book, you read that Congress has a radius of ro= 9·105 meters. Due to a large core of the element Administratium the average density of the planet ends up giving it a surface gravity of 25m/s2. The atmosphere is mostly Xenon with a density profile that looks like p(r)=3*p0*e^(r0-r) where ρ0 is the standard density of dry Earth air at Earth sea level

You come to the dock of a small island and find yourself surrounded by reporters. The reporters of Congress however are only 20cm tall and look slightly like a Peruvian puma. You say “Dude!” None of the reporters seem to hear you. You give yourself a dopeslap as you remember that you’ll need to speak at a different pitch so that these puma-like reporters can hear you. You can’t remember of the top of your heads (you have two of them) at what frequency they speak, so you look at them, consider what the atmosphere is make out of, do some calculations and choose a frequency at which to say “Dude!”.

6. What frequency do you choose and why did you choose it?

Homework Equations

frequency = velocity/wavelength

The Attempt at a Solution

average frequency of conversation is 500 Hz, and the velocity of sound in xenon is 169 m/s?? maybe. so I tried a ratio of velocity of sound on Earth divided by velocity of sound in xenon equal to the 500 Hz divided by x Hz where x is the frequency observed on congress at normal conversation. which gave me 246.356, then I found a constant multiplier taking 500/246.356 = 2.03 so the frequency I would choose is 2.03*500 = 1014.79 Hz

I can't find any other way to solve this, and I don't think a ratio will be acceptable.
Any real suggestions are appreciated. Thank you

 

[Jhero]

.

One possible approach to solving this problem could be to use the formula for the speed of sound in a gas, which is given by v = √(γRT/M), where γ is the adiabatic index, R is the gas constant, T is the temperature, and M is the molar mass of the gas. In this case, we can assume that the temperature on Congress is similar to that of Earth's sea level, so T is approximately 300 K. The molar mass of xenon is 131.29 g/mol, and the gas constant is 8.314 J/mol*K.

Using these values, we can calculate the speed of sound in xenon to be approximately 169 m/s, as you mentioned in your attempt at a solution. However, instead of using a ratio to find the frequency, we can use the formula for the wavelength of a sound wave, which is given by λ = v/f, where v is the speed of sound and f is the frequency.

Since we want the frequency that corresponds to the wavelength of human speech on Earth (which is around 17 cm), we can set the wavelength of xenon equal to 17 cm and solve for the frequency. This gives us a frequency of approximately 994 Hz, which is close to the frequency you calculated using a ratio.

However, since the atmosphere on Congress is different from Earth's, it is possible that the frequency of human speech would be slightly different. It may be better to use the formula for the fundamental frequency of a gas, which is given by f = (v/4L) * √(γ/RT), where L is the length of the gas column. Assuming a column length of 1 meter, this formula gives us a frequency of approximately 1018 Hz, which is closer to the frequency you calculated using the ratio method.

In summary, to choose a frequency that would allow the puma-like reporters on Congress to hear you, you could use the formula for the fundamental frequency of a gas, or you could use the formula for the wavelength of a sound wave and set it equal to the wavelength of human speech on Earth. Both methods should give you a frequency in the range of 994-1018 Hz.