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A guitarist tunes a string against an electronic tone of 196 Hz…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A guitarist tunes a string against an electronic tone of . Together they give 5 beats each second. The guitarist tightens the string a little, and the beats slow to 3 each second. (a) What was the frequency of the string at first? (b) What is it now? (c) What should the guitarist do next?
Need a reminder? The key ideaShow
Two sounds of frequencies and that are close give beats:
You hear the pitch . Wax lowers a fork's frequency, filing raises it, tightening raises a string's.
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.
(a) At first. The string was or . Tightening raises its frequency, and the beats got slower. So it moved towards from below. It was .
(b) Now. 3 beats each second, still below: .
(c) Next. Tighten a little more, until the beats stop. Then the string is at .
Check. Had the string been , tightening would raise it further, and the beats would get faster.
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