I realize that there is a flaw in my reasoning. I don't know what it is. Please point it out(adsbygoogle = window.adsbygoogle || []).push({});

A string is oscillating in a transverse sinusoidal wave. Consider a small element of that string.

When the element of the string has displacement zero, it has the greatest possible kinetic energy and elastic potential energy, and is stretched by the greatest amount possible.

When the element of the string has displacement equal to the amplitude of the wave, it has zero kinetic energy, zero elastic potential energy, and is stretched by the smallest amount possible.

Where is the tension greatest?

The elastic potential energy of the element is greatest when the displacement is zero. Therefore, the tension must be greatest there also.

But wait: F = ma, and the acceleration at displacement zero is also zero, while the acceleration at maximum displacement is the greatest possible amount. The only force the string is subject to is due to tension. Therefore, since the acceleration is greatest when the displacement is equal to the amplitude, the tension must be greatest there also.

Both of these sound perfectly well reasoned to me, and yet are completely mutually exclusive. One or both of them must therefore have a logical error, but what is it?

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# Tension paradox?

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