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 in the string, and μ is the linear density (mass per unit length) of the string.

If the tension is quadrupled, f becomes:

f' = (1/2L) * sqrt(4T/μ) = 2(1/2L) * sqrt(T/μ) = 2f

Therefore, the fundamental frequency becomes twice its original value. 
Hence, the correct choice is E.

The Fundamental Frequency of a Vibrating String Is F1

The Fundamental Frequency of a Vibrating String Is F₁