Sound questions

[TheRealAngeleno]

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Hey guys so I have 2 questions from TBR Physics regarding the speed of sound in a medium. This is the rule they provided;

v is proportional to sqrt (Restoring Force or Molecular K.E. / Molecular Inertia)

I used this to try and solve the following 2 questions;

1) Which of the following changes will increase the speed of sound in a fixed volume of diatomic hydrogen gas that is enclosed?

I. Increase the temperature of the gas.
II. Replace the hydrogen molecules with diatomic oxygen molecules, while holding the temperature constant.
III. Increase the intermolecular attraction between the molecules.

So increasing the temperature would increase the molecular K.E. so statement I is true. Increasing the intermolecular attraction between the molecules would increase the restoring force so statement III would be true. Is my reasoning for statements I & III correct? I can't seem to reason out statement II so could someone please explain why it is false?


2) An acoustic scientist measures the properties of three unknown molecules, labeled A,B, and C. He records the following relationships for the molecular weights and cohesive forces of the molecules:

Ma>Mb=Mc and Fa<Fb<Fc

These relationships hold true, regardless of the state of the material. Noting these results, which of the following relationships could he predict regarding the speed of sound in these materials? (Assume all solids have the same lattice structure and all gases have the same molarity.)

I. Speed of sound is greater in Gas A than Gas B, when both are at the same temperature.
II. Speed of sound is greater in Solid C than Solid B, when both are at the same temperature.
III. Speed of sound in Liquid C is greater than that in Liquid A, when Liquid A is hotter than Liquid C.

So I was able to reason out statements I & II but can't seem to reason out statement III. Could someone please explain why statement III is false? Thanks a lot guys!

 

[tttgo]

For 1, you have the root mean square speed equation that says larger particles move slower.
For 2, molecules have more collisions and move faster at higher temps. When it says regardless of state, they only mean solid, liquid, gas.

 

[TheRealAngeleno]

For 1, you have the root mean square speed equation that says larger particles move slower.
For 2, molecules have more collisions and move faster at higher temps. When it says regardless of state, they only mean solid, liquid, gas.

How would you balance out the increase in temperature with the other factors provided in the question? Like so we know for molecule C it has more cohesive forces and has a smaller MW. So wouldn't the speed of sound be faster in Liquid A only at a certain temperature and not necessarily when it is just hotter?

 

[tttgo]

I think they designed the question so you didn't have to over think it. smaller MW=faster, but larger cohesive force=slower. Maybe the effect of mass outweighs the force here, but that depends on the temperature like you mentioned above. That's why statement 3 doesn't always hold true. I actually misread the question and thought you asked why it was true.