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I am a bit puzzled by a physics problem.

I had to calculate the force on a wire and its second harmonic. Given data were, the diameter of of the string 1,2 mm , length of 1,25m. Density of steel 7,8 kg/dm^3, its fundamental frequency is 300 Hz, and also one end is fixed the other is loose so it can move frictionless up and down.

I know of a very handy equation but it should work when both ends are fixed.

frequency of nth harmonic = nth harmonic/(2 * length of string) * sqrt(force/(density*area))

may I use this equation if the other end is lose? What is the difference when having the other end loose. I never paid much attention to that, I practiced only on both ends fixed, since that makes sense to me. Why would anybody want to have the other end loose?

anyway, I did some algebra on the equation and found that the force should be around 6 kN! I couldnt believe my eyes. Surely I have misscalculated. But oddly, all the people I talked to get even higher value! Most got around 20kN but that is impossible! Imagine having 2 tone weight to put the force needed on a string with diameter 1,2 mm!

Since I am not sure if my reasoning is correct but a steel wire should surely break at such high values! If I recall correctly from reading a text. Breaking Force = Breaking Stress * Area. If I recall Breaking Stress for piano steel wire is at most 2000 MPa or lets say 2 GPa. But that would be an overestimate but never mind. Putting this into the equation I get Breaking Force = 2 * 10^9 * Pi * (0,6 * 10^-3 m)^2= 2,2kN. Wow. But the problem said it was common steel wire soo that is half the value!

Something is wrong here, either my calculations/reasoning, or the problem itself make no sense. Also the people I talked to got the second harmonic to be 900 Hz. Is it just me or is that really really (too) high value?

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# Calculating force on a string and harmonics, something doesnt add up

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