Frequency question (pipe open vs string tied at both ends)

[Crookster]

So I just finished tbr physics chapter on sound and passage 7 question 46 says:

Which will produce the higher frequency a string tied at both ends or a pipe closed at one end?
A. The string
B. The pipe
C. Both produce equal frequencies
D. Not enough info given

Now what's confusing me is the answer they give both equations:

String tied at both ends... f=nv/2L
Pipe open at one end... f=nv/4L

The answer is d (not enough info) I get this because we are not given any info about speed of the waves, but it also says one might be tempted to say that the pipe will always produce a higher frequency because it has a 4 in the denominator? ---how can this be? Wouldn't the 4 in the denominator make the frequency smaller/lower (assuming n and v were held constant) because you are increasing the denominator by a factor of 4 rather than 2 (with the strings equation). Could they have messed this explanation up?

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[aimingforthat45]

yeah, that could be a typo. also, for that question, you can't assume that both the string and pipe are of the same lengths, so you aren't given L, which makes D the best answer.

 

[Crookster]

yeah, that could be a typo. also, for that question, you can't assume that both the string and pipe are of the same lengths, so you aren't given L, which makes D the best answer.

Sorry I forgot to mention they said both lengths were the same (1m, I believe). Thanks for pointing that out.

 

[deleted439911]

In my book (2013 edition), they explained that the wave speed may be different. So you can't assume v is the same.

 

[gettheleadout]

Moving to Q&A.