Standing wave in a column of methane, find gamma of methane

[Taniaz]

Homework Statement

A standing wave with a frequency of 1100 Hz in a column of methane at produces nodes that are 0.200 m apart. What is the value of γ for methane? (The molar mass of methane is 16.0 g/mol)

Homework Equations

v = sqrt ( γRT/M) where R is 8.341, T = 20 °C and M = 16.0 g/mol.
v=fλ for the standing wave

The Attempt at a Solution

From what I understand we have to find the speed of the standing wave and equate it to the speed of methane and solve for γ but the problem is that they've not told us anything about the standing wave, as in how many nodes does it have or the length of the column or if it's open or closed? So how do we calculate the speed of the standing wave?

 

[TSny]

nodes that are 0.200 m apart.

What can you deduce from this?

 

[Taniaz]

The wavelength?

 

[TSny]

Yes, you can determine the wavelength.

 

[Taniaz]

Distance between 2 adjacent nodes is λ/2
But are there just two nodes? Because the answer for gamma is 1.27 and I don't get that.
so λ/2=0.2 so λ=0.4 m
fλ=v=1100 (0.4) = 440 m/s
v= sqrt (γRT/M)
(440)=sqrt ( γ (8.341)(20) / 16)
And I get a really big number for ϒ?

 

[mukundpa]

T is absolute temperature and put proper units for R

 

[Taniaz]

Ohhhhh yess my bad regarding the temperature! Thanks!

 

[mukundpa]

With that think the units of R to be use.

 

[Taniaz]

(440 m/s )^2 = y(8.314 J / mol.K)(20 +273)K / 16 x 10^-3 kg
Now gamma = 1.27
Thanks!