AP Physics 1 Question 308: Answer and Explanation
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6. Both of the above strings have their ends locked in place. The two strings have the same linear density, but the first string, S1, is twice as long as the second string, S2. If sound waves are going to be sent through both, what is the correct ratio of the fundamental frequency of S1 to the fundamental frequency of S2?
- A. 2:1
- C. 1:
- D. 1:2
Correct Answer: D
A wave passing along a string with both ends held in place will have a fundamental frequency of f = v/(2l), where v is the speed of the wave and l is the length of the string. Thus, fundamental frequency is inversely proportional to the length of the string, so the first string, which is twice as long as the second, will have a fundamental frequency that is half of the second string's. Expressed as a ratio, that is 1:2.