A string,fixed at both ends vibrates at a fundamental frequency of 450 Hz and has a mass per unit length of 5.51 * 10^-4 kg/m.The tension in the string is 200 N.What is the length of the string? A)53 cm B)80 cm C)67 cm D)92 cm E)120 cm

Question

Quizplus · Accepted Answer

The formula for the fundamental frequency of a string is:

f = (1/2L) * √(T/μ)

where L is the length of the string, T is the tension in the string, and μ is the mass per unit length of the string.

Rearranging this formula gives:

L = (1/2) * T/(μ * f^2)

Plugging in the given values:

L = (1/2) * (200 N) / (5.51 kg/m * (450 Hz)^2)

L ≈ 0.67 m = 67 cm

Therefore, the correct answer is C, 67 cm.

A String,fixed at Both Ends Vibrates at a Fundamental Frequency