The fundamental frequency of a vibrating string is f₁. If the tension in the string is quadrupled while the linear density is held constant, the fundamental frequency becomes A) f₁. B) 1.2f₁. C) 1.5f₁. D) 1.7f₁. E) 2f₁.

Question

Quizplus · Accepted Answer

The fundamental frequency of a vibrating string is given by f = (1/2L) sqrt(T/μ), where L is the length of the string, T is the tension, and μ is the linear density. If the tension is quadrupled while the linear density is held constant, then the new tension is 4T and the new fundamental frequency is given by f' = (1/2L) sqrt(4T/μ) = 2(1/2L) sqrt(T/μ) = 2f. Therefore, the fundamental frequency becomes 2 times the original value, which is choice E.

The Fundamental Frequency of a Vibrating String Is F1

The Fundamental Frequency of a Vibrating String Is F₁