(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

An open organ pipe (an open/closed configuration) is tuned to a given frequency. A second pipe with both ends open resonates with twice this frequency. What is the ratio of the length of the first pipe to the second pipe?

2. Relevant equations

I used [tex]f_{1}=\frac{v_{1}}{4L_{1}}, f_{2}=\frac{v_{2}}{2L_{2}}[/tex] to relate the lengths and frequencies. In this case f_1 is the open/closed system and f_2 is the open/open system.

3. The attempt at a solution

Since the second frequency is twice the first I tried f_2=2f_1 and inserted those into their respective equations - setting f_2 as 2f_1. So I had:

[tex]f_{1}=\frac{v_{1}}{4L_{1}}, 2f_{1}=\frac{v_{2}}{2L_{2}}[/tex]

Multiplied "f_2" by 2 to get f_1 alone in that equation in order to set them both equal to f_1.

f_2 now becomes [tex]f_{1}=\frac{v_{2}}{4L_{2}}[/tex] after the above operation.

Both equations are now equal to f_1 so the following is true:

[tex]f_{1}=\frac{v_{1}}{4L_{1}}, f_{1}=\frac{v_{2}}{4L_{2}}[/tex]

Then if do a bit of manipulation I get 4L_2/4L_2.

That is how I arrive at my final answer of 1:1 ratio for the two lengths.

Does this look completely wrong? I've always been poor at calculating ratios for some reason.

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# Homework Help: Easy Frequency Question

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