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My AP physics 1 exam is tomorrow. This question is from a practice exam I have but I never really understood the answer

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Using the setup above, a student tests how the tension in a string affects the frequency of the fundamental standing wave (with one antinode). In each trial, with a known mass in the holder, the student adjusts the oscillator frequency to produce the fundamental standing wave. The student notices that as the mass in the holder increases, the string stretches and the total string length, from the oscillator to the mass holder, increases. Which of the following procedures could help the student decide if the string’s total length has a separate effect from the tension on the fundamental frequency?

(A) Repeating the experiment with a string that does not noticeably stretch when the tension is increased

(B) Repeating the experiment but producing standing waves with two antinodes

(C) Repeating the experiment using a different distance between the oscillator and pulley

(D) Repeating the experiment using lighter blocks

The answer is A. But in A we change the tension and keep the string length constant, so what we're really showing is that changing the tension has a separate effect from the string length (not the opposite which is what the question is asking for). Could it be that showing that A has a separate effect from B is the same as showing that B has a separate effect from A? I think choice C is a better fit because it shows that even with a constant string length we may get different results.

Edit: the question comes from an AP physics 1 practice test but the unit concerning waves was removed from the test, but because the question is testing knowledge in an experimental/lab setting it's still important.

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  • $\begingroup$ As @Chemomechanics have answered, if you "decouple" the two variables (tension and string length) you will see how each affects the system under test. For example, if you keep the length constant and you change only tension (like in A) and you find that the results are the same as before you can conclude that string length has no effect on the resulting frequency (this is an example). $\endgroup$
    – ZaellixA
    May 11, 2022 at 18:10

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The question is "Which of the following procedures could help the student decide if the string’s total length has a separate effect from the tension on the fundamental frequency?" [emphasis added].

Changing the string stiffness changes the total length without changing the tension. This decouples the two parameters of interest.

...what we're really showing is that changing the tension has a separate effect from the string length (not the opposite which is what the question is asking for)...

What's the difference? The statement that two things are different (at least in this context) is commutative; if X differs from Y, then Y differs from X.

I think choice C [i.e., repeating the experiment using a different distance between the oscillator and pulley] is a better fit...

The total string length isn't equal to (nor does it scale with) the horizontal string length, so this answer can't be appropriate.

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