sound wave speed question

[tym]

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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:
MWa > MWb = MWc and Fa < Fr < 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 and pressure.
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.
A. II only
B. I and III only
C II and III only
D. I, II, and III

The answer is A. II only.
Why is III wrong? The explanation given by TBR is "because without knowing the temperature (or knowing that it's equal for all mediums), we do not have enough information to determine
the relative speeds of sound." It doesn't really make sense to me.

And for gas, in which situations should we use v = root square (rp/density) = root square (rRT/M) and "stronger the IMFs, the faster the wave moves"? I mean, for example, if Fa>Fb but Ta<Tb. Holding everything else the same, which wave is faster?

Thank you! Any suggestion will be greatly appreciated!!

 

[sps27]

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:
MWa > MWb = MWc and Fa < Fr < 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 and pressure.
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.
A. II only
B. I and III only
C II and III only
D. I, II, and III

The answer is A. II only.
Why is III wrong? The explanation given by TBR is "because without knowing the temperature (or knowing that it's equal for all mediums), we do not have enough information to determine
the relative speeds of sound." It doesn't really make sense to me.

And for gas, in which situations should we use v = root square (rp/density) = root square (rRT/M) and "stronger the IMFs, the faster the wave moves"? I mean, for example, if Fa>Fb but Ta<Tb. Holding everything else the same, which wave is faster?

Thank you! Any suggestion will be greatly appreciated!!

1) for a gas I would say that molecular weight outweighs the cohesive force. The molecules in a gas phase are much further apart and really have not so much influence over one another. So gas A being of higher molecular weight will have a lesser speed of sound as opposed to B. So that one is false.
2) Solid C has the same molecular weight as B so density is the same. However C has a higher cohesive force so the molecular restoring force for C is higher than B, so we can say that speed of sound is higher in C than in A. So this one seems true
3) Liquid A has a higher molecular weight than liquid C, so we can say it is more dense. Speed of sound is inversely proportional to density for any medium so we can say speed of sound in C will be greater than A. That being said, A is hotter than C, which makes the speed of sound in A more than at STP. Cohesive forces here would support the argument that speed of sound in C is more than A. Since there is ambiguity here on two opposing factors, we cannot really say. So this is ambiguous.

Let me know if my reasoning is wrong. It is easy to reason out knowing the answer to a question, but I am with you. It is an ambiguous question.

 

[tym]

1) for a gas I would say that molecular weight outweighs the cohesive force. The molecules in a gas phase are much further apart and really have not so much influence over one another. So gas A being of higher molecular weight will have a lesser speed of sound as opposed to B. So that one is false.
2) Solid C has the same molecular weight as B so density is the same. However C has a higher cohesive force so the molecular restoring force for C is higher than B, so we can say that speed of sound is higher in C than in A. So this one seems true
3) Liquid A has a higher molecular weight than liquid C, so we can say it is more dense. Speed of sound is inversely proportional to density for any medium so we can say speed of sound in C will be greater than A. That being said, A is hotter than C, which makes the speed of sound in A more than at STP. Cohesive forces here would support the argument that speed of sound in C is more than A. Since there is ambiguity here on two opposing factors, we cannot really say. So this is ambiguous.

Let me know if my reasoning is wrong. It is easy to reason out knowing the answer to a question, but I am with you. It is an ambiguous question.

Thanks sps27!!! That makes sense to me!!

And for III, maybe it is wrong just because there are two opposing factors thus the relative speeds cannot be determined.