Frequencies of fundamental standing waves

[ardour]

Homework Statement

Homework Equations

Harmonics equations

The Attempt at a Solution

So, I got (A), which is the answer key is correct, but I'm not sure whether my reasoning is right or not. Would this be considered a closed-end air column question? Anyways, according to the length-wavelength relationships for the harmonics (which can be seen here: http://www.physicsclassroom.com/class/sound/Lesson-5/Closed-End-Air-Columns), an increase
in length will produce an increase in wavelength. Since both columns have the same height of water in them, the speed of sound through both should be the same, right? This means that the taller column will have a lower frequency than the shorter column, which will need a higher frequency to compensate for the shorter height, making the answer (A) f_1. Is my reasoning correct?

 

[kuruman]

Since both columns have the same height of water in them, the speed of sound through both should be the same, right?

That's not the reason. The speed of sound in air as well as in water is the same regardless of the length of the medium in which it travels. These are simply two pipes with one end closed having different lengths.

 

[ardour]

Ok, I understand. Given the rest of the explanation though, is it correct?

 

[kuruman]

Your explanation is not clear, but you are on the right track. However, the statement

Since both columns have the same height of water in them, the speed of sound through both should be the same, right?

implies that if the the height of water is different, the speed of sound will be different. Why should the speed of sound depend on the height of the water column? Try rewriting your explanation to make it more clear. Doing that will help you clarify your ideas in your mind.