Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A string has a tension of and a mass of for each metre. A student says that shaking it twice as fast makes its waves travel twice as fast.
: the medium sets the speed, the source sets the frequency. On a string, . Two waves in step: a path difference of whole wavelengths is loud, of odd half wavelengths is quiet. Beats: each second.
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. (a) .
Step 2. (b) and .
Answer: at both frequencies; the student is wrong. Shaking faster halves the wavelength; the string alone sets the speed.
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