Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A string m long is fixed at both ends and vibrates in its third harmonic. Waves travel along it at m/s. Find the frequency and the wavelength. How many nodes does the string have, counting both ends?
Waves add point by point: y = y1 + y2. Two frequencies close together give beats at a second. A string fixed at both ends has and nodes half a wavelength apart. A square wave is a sum of odd harmonics .
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.
Step 1. The frequency. Hz.
Step 2. The wavelength. m.
Step 3. The nodes. They are m apart: at , , and m.
Step 4. Count. There are nodes. In general, harmonic has nodes.
Answer: Hz, m and nodes.
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