Standing Waves on a String: True/False Questions

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A string stretched between two fixed points can produce standing waves when plucked vertically, which are classified as transverse waves. The highest resonant frequency is indeed referred to as the fundamental frequency, but it is noted that this statement is false in the context of the discussion. Each end of the string must be a node, while the middle can be an antinode, contradicting the claim that it can never be either. Additionally, it is possible for half a wavelength to occupy the length of the string. Clarification is sought on which specific answers are incorrect according to the website's feedback.
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Homework Statement


A string of length L is stretched horizontally between two fixed points. When the string is plucked vertically, standing waves can be formed on the string. Which of the following statements are true about this situation?
True False The waves on the string are transverse waves
True False The highest resonant frequency is called the fundamental
True False Each end of the string must be a node
True False The middle of the string can never be a node or an antinode
True False It is possible for half a wavelength to fill the length of the string



The Attempt at a Solution



Answers are in bold, from reading through the chapter in my book i was able to come up with those answers, now the website says I am wrong but it doesn't tell me which one is wrong. Can any1 maybe help lead me in the right direction?

Thanks
 
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The second one is false.

The fundamental note has the longest wavelength and therefore the lowest frequency.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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