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The five odd harmonics 1, 3, 5, 7 and 9 of a square wave add up, at the middle of a flat top, to…

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Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

The five odd harmonics 1, 3, 5, 7 and 9 of a square wave add up, at the middle of a flat top, to $\dfrac{4}{\pi}\left(1 - \dfrac{1}{3} + \dfrac{1}{5} - \dfrac{1}{7} + \dfrac{1}{9}\right)$ . How high does the sum reach, and how far is that from the true height of 1?

Need a reminder? The key ideaShow

Waves add point by point: y = y1 + y2. Two frequencies close together give beats at $|f_1 - f_2|$ a second. A string fixed at both ends has $f_n = \dfrac{nv}{2L}$ and nodes half a wavelength apart. A square wave is a sum of odd harmonics $\dfrac{4}{\pi}\dfrac{\sin(mx)}{m}$ .

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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